Miklós Z. Rácz –
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Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
Perfect Filtering and Double Disjointness
ANNALES DE L’I. H. P., SECTION B HILLEL FURSTENBERG YUVAL PERES BENJAMIN WEISS Perfect filtering and double disjointness Annales de l’I. H. P., section B, tome 31, no 3 (1995), p. 453-465 <http://www.numdam.org/item?id=AIHPB_1995__31_3_453_0> © Gauthier-Villars, 1995, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section B » (http://www.elsevier.com/locate/anihpb) implique l’accord avec les condi- tions générales d’utilisation (http://www.numdam.org/conditions). Toute uti- lisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Ann. Inst. Henri Poincaré, Vol. 31, n° 3, 1995, p. 453-465. Probabilités et Statistiques Perfect filtering and double disjointness Hillel FURSTENBERG, Yuval PERES (*) and Benjamin WEISS Institute of Mathematics, the Hebrew University, Jerusalem. ABSTRACT. - Suppose a stationary process ~ Un ~ is used to select from several stationary processes, i.e., if Un = i then we observe Yn which is the n’th variable in the i’th process. when can we recover the selecting sequence ~ Un ~ from the output sequence ~Yn ~ ? RÉSUMÉ. - Soit ~ Un ~ un processus stationnaire utilise pour la selection de plusieurs processus stationnaires, c’ est-a-dire si Un = i alors on observe Yn qui est le n-ième variable dans le i-ième processus. Quand peut-on reconstruire ~ Un ~ à partir de ~ Yn ~ ? 1. INTRODUCTION Suppose a discrete-time stationary stochastic signal ~ Un ~, taking integer values, is transmitted over a noisy channel. -
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Volume 47 • Issue 1 IMS Bulletin January/February 2018 National Academy new member The US National Academy of Medicine (NAM) has announced the election of 70 reg- CONTENTS ular members and 10 international members. Among them is Nicholas Patrick Jewell, 1 National Academy of University of California, Berkeley. Medicine elects Jewell Election to the Academy is considered one of the highest honors in the fields of 2 Members’ news: Nick Horton, health and medicine, recognizing individuals who have made major contributions to Eric Kolaczyk, Hongzhe Li, the advancement of the medical sciences, health care, and public health. A diversity Runze Li, Douglas Simpson, of talent among NAM’s membership is Greg Lawler, Mike Jordan, Mir assured by its Articles of Organization, Masoom Ali which stipulate that at least one-quarter 3 Journal news: EJP, ECP, Prob of the membership is selected from fields Surveys; OECD guidelines outside the health professions, for exam- 4 Takis Konstantopoulos: new ple, from law, engineering, social sciences, column and the humanities—and statistics. The newly elected members bring 6 Recent papers: Electronic Journal of Probability; Electronic NAM’s total membership to 2,127 and Communications in Probability the number of international members to 172. 11 Special Invited Lecturers; IMS Fellow Nicholas P. Jewell is New Textbook Professor of Biostatistics and Statistics 12 Obituary: Ron Getoor at the University of California, Berkeley. 13 IMS Awards Since arriving at Berkeley in 1981, he has held various academic and administrative 15 Student Puzzle Corner 19; New Researcher Award positions, most notably serving as Vice Provost from 1994 to 2000. -
Russell David Lyons
Russell David Lyons Education Case Western Reserve University, Cleveland, OH B.A. summa cum laude with departmental honors, May 1979, Mathematics University of Michigan, Ann Arbor, MI Ph.D., August 1983, Mathematics Sumner Myers Award for best thesis in mathematics Specialization: Harmonic Analysis Thesis: A Characterization of Measures Whose Fourier-Stieltjes Transforms Vanish at Infinity Thesis Advisers: Hugh L. Montgomery, Allen L. Shields Employment Indiana University, Bloomington, IN: James H. Rudy Professor of Mathematics, 2014{present. Indiana University, Bloomington, IN: Adjunct Professor of Statistics, 2006{present. Indiana University, Bloomington, IN: Professor of Mathematics, 1994{2014. Georgia Institute of Technology, Atlanta, GA: Professor of Mathematics, 2000{2003. Indiana University, Bloomington, IN: Associate Professor of Mathematics, 1990{94. Stanford University, Stanford, CA: Assistant Professor of Mathematics, 1985{90. Universit´ede Paris-Sud, Orsay, France: Assistant Associ´e,half-time, 1984{85. Sperry Research Center, Sudbury, MA: Researcher, summers 1976, 1979. Hampshire College Summer Studies in Mathematics, Amherst, MA: Teaching staff, summers 1977, 1978. Visiting Research Positions University of Calif., Berkeley: Visiting Miller Research Professor, Spring 2001. Microsoft Research: Visiting Researcher, Jan.{Mar. 2000, May{June 2004, July 2006, Jan.{June 2007, July 2008{June 2009, Sep.{Dec. 2010, Aug.{Oct. 2011, July{Oct. 2012, May{July 2013, Jun.{Oct. 2014, Jun.{Aug. 2015, Jun.{Aug. 2016, Jun.{Aug. 2017, Jun.{Aug. 2018. Weizmann Institute of Science, Rehovot, Israel: Rosi and Max Varon Visiting Professor, Fall 1997. Institute for Advanced Studies, Hebrew University of Jerusalem, Israel: Winston Fellow, 1996{97. Universit´ede Lyon, France: Visiting Professor, May 1996. University of Wisconsin, Madison, WI: Visiting Associate Professor, Winter 1994. -
"Real Analysis in Computer Science" (Fall 2013) Final Program Report Elchanan Mossel and Luca Trevisan (Organizers) Ba
"Real Analysis in Computer Science" (Fall 2013) Final Program Report Elchanan Mossel and Luca Trevisan (Organizers) Background Sophisticated tools in Real Analysis have played an increasingly central role in a number of areas in theoretical computer science over the past thirty years. As a first example, the discrete Fourier expansion can be used to analyze combinatorial problems of a discrete nature using the language and techniques of real analysis. Such Fourier analysis techniques have played a key role since the 1980s in the development of computational learning theory (PAC learning) and property testing, and, in complexity theory, they have led to circuit lower bounds and to probabilistically checkable proof (PCP) constructions and hardness of approximation results. More modern mathematical tools developed to study Banach space properties of Gaussian processes in the 1960s and 70s (in particular, the idea of hypercontractivity from functional analysis) were introduced in computer science by Kahn, Kalai and Linial in 1988. This circle of ideas played a key role in subsequent developments in coding theory, metric embeddings of graphs, and hardness of approximation of optimization problems. Finally, concepts from Gaussian geometry and Gaussian isoperimetric theory have played an implicit role in the analysis of semi-definite programs, starting with the work of Goemans and Williamson in 1995. A rigorous theory connecting optimization problems, semi-definite programs and hardness of approximation to Gaussian geometry and isoperimetry was established in the “Unique Games” framework introduced by Khot in 2002, and was further developed via the non-linear invariance principle of Mossel, O’Donnell and Oleszkiewicz (2005) and the geometry of Gaussian space. -
Affine Embeddings of Cantor Sets on the Line Arxiv:1607.02849V3
Affine Embeddings of Cantor Sets on the Line Amir Algom August 5, 2021 Abstract Let s 2 (0; 1), and let F ⊂ R be a self similar set such that 0 < dimH F ≤ s . We prove that there exists δ = δ(s) > 0 such that if F admits an affine embedding into a homogeneous self similar set E and 0 ≤ dimH E − dimH F < δ then (under some mild conditions on E and F ) the contraction ratios of E and F are logarithmically commensurable. This provides more evidence for Conjecture 1.2 of Feng et al.(2014), that states that these contraction ratios are logarithmically commensurable whenever F admits an affine embedding into E (under some mild conditions). Our method is a combination of an argument based on the approach of Feng et al.(2014) with a new result by Hochman(2016), which is related to the increase of entropy of measures under convolutions. 1 Introduction Let A; B ⊂ R. We say that A can be affinely embedded into B if there exists an affine map g : R ! R; g(x) = γ · x + t for γ 6= 0; t 2 R, such that g(A) ⊆ B. The motivating problem of this paper to show that if A and B are two Cantor sets and A can be affinely embedded into B, then the there should be some arithmetic dependence between the scales appearing in the multiscale structures of A and B. This phenomenon is known to occur e.g. when A and B are two self similar sets satisfying the strong separation condition that are Lipschitz equivalent, see Falconer and Marsh(1992). -
Characterization of Cutoff for Reversible Markov Chains
Characterization of cutoff for reversible Markov chains Riddhipratim Basu ∗ Jonathan Hermon y Yuval Peres z Abstract A sequence of Markov chains is said to exhibit (total variation) cutoff if the conver- gence to stationarity in total variation distance is abrupt. We consider reversible lazy chains. We prove a necessary and sufficient condition for the occurrence of the cutoff phenomena in terms of concentration of hitting time of \worst" (in some sense) sets of stationary measure at least α, for some α (0; 1). 2 We also give general bounds on the total variation distance of a reversible chain at time t in terms of the probability that some \worst" set of stationary measure at least α was not hit by time t. As an application of our techniques we show that a sequence of lazy Markov chains on finite trees exhibits a cutoff iff the product of their spectral gaps and their (lazy) mixing-times tends to . 1 Keywords: Cutoff, mixing-time, finite reversible Markov chains, hitting times, trees, maximal inequality. arXiv:1409.3250v4 [math.PR] 18 Feb 2015 ∗Department of Statistics, UC Berkeley, California, USA. E-mail: [email protected]. Supported by UC Berkeley Graduate Fellowship. yDepartment of Statistics, UC Berkeley, USA. E-mail: [email protected]. zMicrosoft Research, Redmond, Washington, USA. E-mail: [email protected]. 1 1 Introduction In many randomized algorithms, the mixing-time of an underlying Markov chain is the main component of the running-time (see [21]). We obtain a tight bound on tmix() (up to an absolute constant independent of ) for lazy reversible Markov chains in terms of hitting times of large sets (Proposition 1.7,(1.6)). -
Amber L. Puha, Phd June 2021 Department of Mathematics Craven Hall 6130 California State University San Marcos Office Phone: 1-760-750-4201 333 S
Amber L. Puha, PhD June 2021 Department of Mathematics Craven Hall 6130 California State University San Marcos Office Phone: 1-760-750-4201 333 S. Twin Oaks Valley Road Department Phone: 1-760-750-8059 San Marcos, CA 92096-0001 https://faculty.csusm.edu/apuha/ [email protected] Appointments 2010{present, Professor, Department of Mathematics, CSU San Marcos 2020-2021, Sabbatical Leave of Absence, Research Associate and Teaching Visitor Department of Mathematics, UCSD 2013-2014, Sabbatical Leave of Absence, Research Associate and Teaching Visitor Department of Mathematics, UCSD 2010-2011, Professional Leave of Absence 2009{2011, Associate Director, Institute for Pure and Applied Mathematics (IPAM), UCLA 2004-2010, Associate Professor, Department of Mathematics, CSU San Marcos 2009-2010, Professional Leave of Absence 2005-2006, Sabbatical Leave of Absence, Research Associate and Teaching Visitor, Department of Mathematics, UCSD 1999-2004, Assistant Professor, Department of Mathematics, CSU San Marcos 2000-2001 & Spring 2002, Professional Leave of Absence, National Science Foundation Mathematical Sciences Postdoctoral Fellow Research Interests Probability Theory and Stochastic Processes, with emphasis on Stochastic Networks Professional Awards 2021-2024, PI, National Science Foundation Single-Investigator Award, DMS-2054505, $232,433 2020{2021, CSUSM Research, Scholarship and Creative Activity (RSCA) Grant, $7,200 2019{2020, CSUSM Research, Scholarship and Creative Activity (RSCA) Grant, $2,000 2019, National Scholastic Surfing Association, -
Front Matter
Cambridge University Press 978-1-107-13411-9 — Fractals in Probability and Analysis Christopher J. Bishop , Yuval Peres Frontmatter More Information CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS 162 Editorial Board B. BOLLOBAS,´ W. FULTON, F. KIRWAN, P. SARNAK, B. SIMON, B. TOTARO FRACTALS IN PROBABILITY AND ANALYSIS A mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the Traveling Salesman Theorem. The broad range of techniques presented enables key ideas to be highlighted, without the distraction of excessive technicalities. The authors incorporate some novel proofs which are simpler than those available elsewhere. Where possible, chapters are designed to be read independently so the book can be used to teach a variety of courses, with the clear structure offering students an accessible route into the topic. Christopher J. Bishop is a professor in the Department of Mathematics at Stony Brook University. He has made contributions to the theory of function algebras, Kleinian groups, harmonic measure, conformal and quasiconformal mapping, holomorphic dynamics and computational geometry. Yuval Peres is a Principal Researcher at Microsoft Research in Redmond, WA. He is particularly known for his research in topics such as fractals and Hausdorff measure, random walks, Brownian motion, percolation and Markov chain mixing times. In 2016 he was elected to the National Academy of Science. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-13411-9 — Fractals in Probability and Analysis Christopher J. -
Information Theory and Concentration Phenomena
IMA Workshops April 13-17, 2015 Information Theory and Concentration Phenomena ORGANIZERS SPEAKERS Sergey Bobkov, University of Minnesota, Twin Cities Andrew Barron, Yale University Michel Ledoux, Université de Toulouse (Paul Ronen Eldan, University of Washington Sabatier) Larry Goldstein, University of Southern California Joel Tropp, California Institute of Technology Oliver Johnson, University of Bristol Bo’az Klartag, Tel Aviv University Holger Kösters, Universität Bielefeld Concentration phenomena have come to play Victoria Kostina, California Institute of a significant role in probability, statistics, and Technology Rafal Latala, University of Warsaw computer science. Ideas from information theory Katalin Marton, Hungarian Academy of and geometry can be used to establish new Sciences (MTA) types of concentration inequalities. At the same Elizabeth Meckes, Case Western time, concentration results can lead to a deeper Reserve University understanding of information theory and geometry. Emanuel Milman, Technion-Israel Institute of Technology Although these principles are well established, there Andrea Montanari, Stanford University have been many striking advances in recent years. Elchanan Mossel, University of Researchers have made significant progress on California, Berkeley subadditivity of quantum information, quantitative Roberto Oliveira, Institute of Pure and entropy power inequalities, and concentration Applied Mathematics (IMPA) properties for random variables that have many Grigorios Paouris, Texas A & M University symmetries -
CHRISTOPHER J. BISHOP Department of Mathematics Stony Brook University Stony Brook, NY 11794-3651
CHRISTOPHER J. BISHOP Department of Mathematics Stony Brook University Stony Brook, NY 11794-3651 RESEARCH INTERESTS Real and complex analysis, geometric function theory, conformal dynamics, probability theory, numerical analysis, analysis on fractals, quasiconformal geometry, computational geometry. Some of my more particular interests have included: potential theory, fractal properties of harmonic measure, geometric properties of Brownian motion and other random processes, al- gebras generated by harmonic and holomorphic functions, geometry of hyperbolic manifolds and their covering groups, numerical computation of conformal mappings, multipole methods, optimal meshing algorithms, nonobtuse triangulation, quadrilateral meshing, iteration of entire functions and dimension distorting properties of quasiconformal maps. I program in C, Mathe- matica and Matlab as part of my investigations in these areas, and teach a class on experimental aspects of mathematics. PROFESSIONAL EXPERIENCE Sept. 1997 to present: Professor at Stony Brook University. Sept. 1992 to Aug. 1997: Assoc. professor at Stony Brook. Sept. 1991 to Aug. 1992: Asst. professor at Stony Brook. Sept. 1988 to Aug. 1991: Hedrick Asst. professor at UCLA. Sept. 1987 to Aug. 1988: NSF postdoc at MSRI, Berkeley. EDUCATION Cambridge University, Master of Advanced Study (MASt), 2011. University of Chicago, Mathematics, Ph. D., 1987, Advisor Peter W. Jones. Visiting graduate student and programmer, Dept. of Mathematics, Yale University, 1985-1987. University of Chicago, Mathematics, Master of Science, 1984. Cambridge University, Certificate of Advanced Study (Part III of Math. Tripos), 1983. Michigan State University, Mathematics, Bachelor of Science, 1982. PH.D. STUDENTS Zsuzsanna Gonye, Ph. D. 2001, Geodesics in hyperbolic manifolds, Assoc. Professor, University of West Hungary Karyn Lundberg, Ph. D. 2005, Boundary behavior of conformal mappings, researcher, Lincoln Labs Hrant Hakobyan, Ph.D. -
Diffusive Estimates for Random Walks on Stationary Random Graphs Of
Diffusive estimates for random walks on stationary random graphs of polynomial growth Shirshendu Ganguly ∗ James R. Lee y Yuval Peres z Abstract G Let (G; ρ) be a stationary random graph, and use Bρ (r) to denote the ball of radius r about ρ G k in G. Suppose that (G; ρ) has annealed polynomial growth, in the sense that E[ Bρ (r) ] 6 O(r ) for some k > 0 and every r > 1. j j Then there is an infinite sequence of times tn at which the random walk Xt on (G; ρ) is at most diffusive: Almost surely (over the choicef ofg (G; ρ)), there is a number C f> 0g such that h 2 i E distG(X ; Xt ) X = ρ, (G; ρ) 6 Ctn n > 1 : 0 n j 0 8 This result is new even in the case when G is a stationary random subgraph of Zd. Combined with the work of Benjamini, Duminil-Copin, Kozma, and Yadin (2015), it implies that G almost surely does not admit a non-constant harmonic function of sublinear growth. To complement this, we argue that passing to a subsequence of times tn is necessary, as there are stationary random graphs of (almost sure) polynomial growth wheref theg random walk is almost surely superdiffusive at an infinite subset of times. Contents 1 Introduction 2 1.1 The absence of non-constant sublinear growth harmonic functions..........3 1.2 Speed via Euclidean embeddings..............................4 1.3 A deterministic example: Planar graphs..........................6 2 Martingales, embeddings, and growth rates8 2.1 Control by martingales....................................9 2.2 Embeddings and growth rates...............................