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Cambridge University Press 978-0-521-14735-4 - Probability on Graphs: Random Processes on Graphs and Lattices Geoffrey Grimmett Frontmatter More information Probability on Graphs This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm–Lowner¨ evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov’s proof of Cardy’s formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises. geoffrey grimmett is Professor of Mathematical Statistics in the Statistical Laboratory at the University of Cambridge. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-14735-4 - Probability on Graphs: Random Processes on Graphs and Lattices Geoffrey Grimmett Frontmatter More information INSTITUTE OF MATHEMATICAL STATISTICS TEXTBOOKS Editorial Board D. R. Cox (University of Oxford) B. Hambly (University of Oxford) S. Holmes (Stanford University) X.-L. Meng (Harvard University) IMS Textbooks give introductory accounts of topics of current concern suitable for advanced courses at master’s level, for doctoral students and for individual study. -
June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings for MATHEMATICS 2014 and Events Following a Very Generous Tions Open in Late 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 437 June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings FOR MATHEMATICS 2014 and Events Following a very generous tions open in late 2014. The prize Monday 16 June donation made by Professor may be awarded to either a single Midlands Regional Meeting, Loughborough Geoffrey Shephard, the London winner or jointly to collaborators. page 11 Mathematical Society will, in 2015, The mathematical contribution Friday 4 July introduce a new prize. The prize, to which an award will be made Graduate Student to be known as the Shephard must be published, though there Meeting, Prize will be awarded bienni- is no requirement that the pub- London ally. The award will be made to lication be in an LMS-published page 8 a mathematician (or mathemati- journal. Friday 4 July cians) based in the UK in recog- Professor Shephard himself is 1 Society Meeting nition of a specific contribution Professor of Mathematics at the Hardy Lecture to mathematics with a strong University of East Anglia whose London intuitive component which can be main fields of interest are in page 9 explained to those with little or convex geometry and tessella- Wednesday 9 July no knowledge of university math- tions. Professor Shephard is one LMS Popular Lectures ematics, though the work itself of the longest-standing members London may involve more advanced ideas. of the LMS, having given more page 17 The Society now actively en- than sixty years of membership. Tuesday 19 August courages members to consider The Society wishes to place on LMS Meeting and Reception nominees who could be put record its thanks for his support ICM 2014, Seoul forward for the award of a in the establishment of the new page 11 Shephard Prize when nomina- prize. -
Probability on Graphs Random Processes on Graphs and Lattices
Probability on Graphs Random Processes on Graphs and Lattices GEOFFREY GRIMMETT Statistical Laboratory University of Cambridge c G. R. Grimmett 1/4/10, 17/11/10, 5/7/12 Geoffrey Grimmett Statistical Laboratory Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB United Kingdom 2000 MSC: (Primary) 60K35, 82B20, (Secondary) 05C80, 82B43, 82C22 With 44 Figures c G. R. Grimmett 1/4/10, 17/11/10, 5/7/12 Contents Preface ix 1 Random walks on graphs 1 1.1 RandomwalksandreversibleMarkovchains 1 1.2 Electrical networks 3 1.3 Flowsandenergy 8 1.4 Recurrenceandresistance 11 1.5 Polya's theorem 14 1.6 Graphtheory 16 1.7 Exercises 18 2 Uniform spanning tree 21 2.1 De®nition 21 2.2 Wilson's algorithm 23 2.3 Weak limits on lattices 28 2.4 Uniform forest 31 2.5 Schramm±LownerevolutionsÈ 32 2.6 Exercises 37 3 Percolation and self-avoiding walk 39 3.1 Percolationandphasetransition 39 3.2 Self-avoiding walks 42 3.3 Coupledpercolation 45 3.4 Orientedpercolation 45 3.5 Exercises 48 4 Association and in¯uence 50 4.1 Holley inequality 50 4.2 FKGinequality 53 4.3 BK inequality 54 4.4 Hoeffdinginequality 56 c G. R. Grimmett 1/4/10, 17/11/10, 5/7/12 vi Contents 4.5 In¯uenceforproductmeasures 58 4.6 Proofsofin¯uencetheorems 63 4.7 Russo'sformulaandsharpthresholds 75 4.8 Exercises 78 5 Further percolation 81 5.1 Subcritical phase 81 5.2 Supercritical phase 86 5.3 Uniquenessofthein®nitecluster 92 5.4 Phase transition 95 5.5 Openpathsinannuli 99 5.6 The critical probability in two dimensions 103 5.7 Cardy's formula 110 5.8 The -
Scheme of Instruction 2021 - 2022
Scheme of Instruction Academic Year 2021-22 Part-A (August Semester) 1 Index Department Course Prefix Page No Preface : SCC Chair 4 Division of Biological Sciences Preface 6 Biological Science DB 8 Biochemistry BC 9 Ecological Sciences EC 11 Neuroscience NS 13 Microbiology and Cell Biology MC 15 Molecular Biophysics Unit MB 18 Molecular Reproduction Development and Genetics RD 20 Division of Chemical Sciences Preface 21 Chemical Science CD 23 Inorganic and Physical Chemistry IP 26 Materials Research Centre MR 28 Organic Chemistry OC 29 Solid State and Structural Chemistry SS 31 Division of Physical and Mathematical Sciences Preface 33 High Energy Physics HE 34 Instrumentation and Applied Physics IN 38 Mathematics MA 40 Physics PH 49 Division of Electrical, Electronics and Computer Sciences (EECS) Preface 59 Computer Science and Automation E0, E1 60 Electrical Communication Engineering CN,E1,E2,E3,E8,E9,MV 68 Electrical Engineering E0,E1,E4,E5,E6,E8,E9 78 Electronic Systems Engineering E0,E2,E3,E9 86 Division of Mechanical Sciences Preface 95 Aerospace Engineering AE 96 Atmospheric and Oceanic Sciences AS 101 Civil Engineering CE 104 Chemical Engineering CH 112 Mechanical Engineering ME 116 Materials Engineering MT 122 Product Design and Manufacturing MN, PD 127 Sustainable Technologies ST 133 Earth Sciences ES 136 Division of Interdisciplinary Research Preface 139 Biosystems Science and Engineering BE 140 Scheme of Instruction 2021 - 2022 2 Energy Research ER 144 Computational and Data Sciences DS 145 Nanoscience and Engineering NE 150 Management Studies MG 155 Cyber Physical Systems CP 160 Scheme of Instruction 2020 - 2021 3 Preface The Scheme of Instruction (SoI) and Student Information Handbook (Handbook) contain the courses and rules and regulations related to student life in the Indian Institute of Science. -
David Blackwell Instance for Activities That Could Run Sometime Between Now and the End of June 2012
Volume 39 • Issue 8 IMS1935–2010 Bulletin October 2010 IMS Short Courses Proposal New IMS President Peter Hall outlines a proposed IMS program of short courses and Contents short meetings: 1 IMS Short Courses The IMS is considering developing a program of short courses and short meetings, reflecting all of the research areas encompassed by our journals. The motivation is at 2–3 Members’ News: Marta Sanz- Solé; David Brillinger; PK Sen; Elizaveta least two-fold. Firstly, we are not very widely involved in specialist meetings, and from Levina; Jerry Friedman; Samuel Kou; this point of view our scientific leadership can probably be enhanced. Secondly, in the Emily Berg; Wayne Fuller; Xuming He; area of short courses, there is an opportunity for both the IMS and its members to earn Jun Liu; Yajun Mei, Nicoleta Serban, a little extra income, by sharing the profits earned by delivering those courses. Roshan Joseph Vengazihiyil, Ming Yuan The best way in which to operate our short courses and short meetings will prob- ably be learned over time, but a few principles can be predicted in advance. In particu- 4 IMS 2010 Gothenburg meeting report & photos lar, the short courses and meetings should be held in places not in direct competition with relevant, major existing conferences, for example the Joint Statistical Meetings. Of 6 Peking University’s Center course, there are many opportunities for avoiding clashes such as these. The concept of for Statistical Science “IMS Winter Workshops” in North America, perhaps held in early January in southern 7 Conference in memory of US, is only one suggestion. -
Postmaster and the Merton Record 2019
Postmaster & The Merton Record 2019 Merton College Oxford OX1 4JD Telephone +44 (0)1865 276310 www.merton.ox.ac.uk Contents College News Edited by Timothy Foot (2011), Claire Spence-Parsons, Dr Duncan From the Acting Warden......................................................................4 Barker and Philippa Logan. JCR News .................................................................................................6 Front cover image MCR News ...............................................................................................8 St Alban’s Quad from the JCR, during the Merton Merton Sport ........................................................................................10 Society Garden Party 2019. Photograph by John Cairns. Hockey, Rugby, Tennis, Men’s Rowing, Women’s Rowing, Athletics, Cricket, Sports Overview, Blues & Haigh Awards Additional images (unless credited) 4: Ian Wallman Clubs & Societies ................................................................................22 8, 33: Valerian Chen (2016) Halsbury Society, History Society, Roger Bacon Society, 10, 13, 36, 37, 40, 86, 95, 116: John Cairns (www. Neave Society, Christian Union, Bodley Club, Mathematics Society, johncairns.co.uk) Tinbergen Society 12: Callum Schafer (Mansfield, 2017) 14, 15: Maria Salaru (St Antony’s, 2011) Interdisciplinary Groups ....................................................................32 16, 22, 23, 24, 80: Joseph Rhee (2018) Ockham Lectures, History of the Book Group 28, 32, 99, 103, 104, 108, 109: Timothy Foot -
Probability on Graphs: Random Processes on Graphs and Lattices, by Geoffrey Grim- Mett, Institute of Mathematical Statistics Textbooks, Vol
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 51, Number 1, January 2014, Pages 173–175 S 0273-0979(2013)01428-9 Article electronically published on July 26, 2013 Probability on graphs: random processes on graphs and lattices, by Geoffrey Grim- mett, Institute of Mathematical Statistics Textbooks, Vol. 1, Cambridge Univer- sity Press, Cambridge, 2010, xii+247 pp., ISBN 978-0-521-14735-4, paperback, US$38.99 Growth of the field of mathematics called Interacting Particle Systems (IPS) was, to a great extent, catalyzed by Liggett’s 1985 monograph [12]. Thirty years later this IPS field (together with the closely related percolation field) remains an active area within mathematical probability and the theorem-proof end of statistical physics, with its MSC primary classification 60K35 containing about 170 papers a year. In brief, IPS studies models over a graph: each vertex (or site)isinsome state; vertices interact with neighboring vertices at random intervals and update their states according to some rule. For instance in the contact process,anatural toy model for epidemics, a vertex is either infected or healthy: healthy sites become infected at rate λ times the number of infected neighbors, and infected sites become healthy at constant rate one (rate means probability per unit time). Liggett’s book gave a masterful account of work on several models over the previous 15 years, for which a major original motivation had been rigorous study of the statistical physics notion of phase transitions, formalized as qualitative changes in behavior of a process defined on the infinite d-dimensional lattice as parameters pass through a critical value. -
Newsletter of The
Number 114 May 2012 NEWSLETTER OF THE NEWZEALANDMATHEMATICALSOCIETY Contents PUBLISHER'S NOTICE....................... 2 PRESIDENT'S COLUMN...................... 3 EDITORIAL .............................. 3 CONTRIBUTED EDITORIAL ................... 4 LOCAL NEWS ............................ 8 CENTREFOLD ............................ 18 MATHEMATICAL MINIATURE ................. 20 LOCAL NEWS continues ...................... 22 FEATURES .............................. 29 CONFERENCES ........................... 33 PUBLISHER'S NOTICE PUBLISHER'S NOTICE This newsletter is the official organ of the New Zealand Mathematical Society Inc. This issue was edited by Steven Archer and printed at Victoria University of Wellington. The official address of the Society is: The New Zealand Mathematical Society, c/- The Royal Society of New Zealand, P.O. Box 598, Wellington, New Zealand. However, correspondence should normally be sent to the Secretary: Dr Alex James Department of Mathematics and Statistics University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand [email protected] NZMS Council and Officers President Dr Graham Weir (Industrial Research Limited) Immediate Past President Prof Charles Semple (University of Canterbury) Secretary Dr Alex James (University of Canterbury) Treasurer Dr Peter Donelan (Victoria University of Wellington) Councillors Dr Boris Baeumer (University of Otago) Assoc Prof Bruce van Brunt (Massey University) Dr Tom ter Elst (University of Auckland) Prof Astrid an Huef (University of Otago) Prof Robert McKibbin -
David Haussler Elected to NAS IMS Member David Haussler Is One of 72 New Mem- Contents Bers Elected to the US National Academy of Sciences
Volume 35 Issue 5 IMS Bulletin June 2006 David Haussler elected to NAS IMS member David Haussler is one of 72 new mem- CONTENTS bers elected to the US National Academy of Sciences. 1 David Haussler, NAS Members are chosen in recognition of their distin- guished and continuing achievements in original 2 IMS Members’ News: Bin Yu, Hongyu Zhao, research. Ralph Cicerone, Academy president, says, Jianqing Fan “Election to the Academy is considered one of the highest honors in American science and engineering.” 4 LNMS Sale David Haussler is an investigator with the 5 IMS news Howard Hughes Medical Institute and a professor 6 Rio guide: eating, dancing, of biomolecular engineering at the University of having fun California, Santa Cruz, where he directs the Center David Haussler, recently elected to the for Biomolecular Science & Engineering. He serves 7 SSP report US National Academy of Sciences as scientific co-director for the California Institute 8 Terence’s Stuff: The Big for Quantitative Biomedical Research (QB3), and he is a consulting professor at Question both Stanford Medical School and UC San Francisco Biopharmaceutical Sciences 9 Meet the Members Department. David was recently elected to the American Academy of Arts and Sciences; 10 JSM News: IMS Invited Program highlights he is also a fellow of both AAAS and AAAI. He has won a number of prestigious awards, including recently the 2006 Dickson Prize for Science from Carnegie Mellon IMS Meetings 12 University. David received his BA degree in mathematics from Connecticut College 19 Other Meetings and in 1975, an MS in applied mathematics from California Polytechnic State University Announcements at San Luis Obispo in 1979, and his PhD in computer science from the University of 21 Employment Colorado at Boulder in 1982. -
September 1988 Table of Contents
OTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1988 Steele Prizes page 965 ;I~ The AMS Centennial: Social and Mathematical Festivities page 970 SEPTEMBER 1988, VOLUME 35, NUMBER 7 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting. Abstracts should be sub and annual meetings are joint meetings of the Mathematical Associ mitted on special forms which are available in many departments of ation of America and the American Mathematical Society. The meet mathematics and from the headquarters office of the Society. Ab ing dates which fall rather far in the future are subject to change; this stracts of papers to be presented at the meeting must be received is particularly true of meetings to which no numbers have been as at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated or before the deadline given below for the meeting. Note that the below. First and supplementary announcements of the meetings will deadline for abstracts for consideration for presentation at special have appeared in earlier issues. sessions is usually three weeks earlier than that specified below. For Abstracts of papers presented at a meeting of the Society are pub additional information, consult the meeting announcements and the lished in the journal Abstracts of papers presented to the American list of organizers of special sessions. -
15/14/39 Liberal Arts and Sciences Mathematics Department Donald L. Burkholder Papers, 1947-2011 Box 1
15/14/39 Liberal Arts and Sciences Mathematics Department Donald L. Burkholder Papers, 1947-2011 Box 1: Biographical File CORRESPONDENCE--This correspondence file contains confidential information, and access requires approval from an archivist. Family, 1961-92 Politics (includes letters from Senators Paul Douglas and Everett McKinley Dirksen regarding civil rights legislation), 1963-64 Professional, 1956-75 1959-65 1962-64 1967 1968-71 1969-70 1973-76 1981-86 1987-91 1992-94 1994-2003 2004-2011 By Correspondent David Aldous, 1979-81 A. N. Al-Hussaini, 1964-2003 Dale Alspach, 1985-89 Madjid Amir, 1989-94 F. Amoroso, 1996 George Anastassiou, 1991 T. W. Anderson, 1965 T. Ando, 1983 J. Arazy, 1978-91 Ludwig Arnold, 1993-94 J. Marshall Ash, 1986-87 Nakhle Asmar, 1992-97 Idris Assani, 1986-95 Robert J. Aumann, 1986 Don G. Austin, 1966 Al Baernstein, 1975-2003 R. R. Bahadur, 1997 Rodrigo Banuelos, 1985-2005 (4 folders) 15/14/39 2 Box 2: 1985-2005 (4 folders) Martin Barlow, 1990-95 (2 folders) Richard Bass, 1985-2007 (2 folders) J. G. Basterfield, 1972 Robert Bauer, 1994-2003 (3 folders) Bernard Beauzamy, 1986-2008 (5 folders) William Beckner, 1980-88 Denis Bell, 1995-97 Alexandra Bellow, 1965-2001 Box 3: 1965-2001 John Benedetto, 1996 Andrew Bennett, 1986-87 Colin Bennett, 1994 Robert Berk, 1967-68 Klaus Bichteler, 1981-92 P. Billard, 1972 N. H. Bingham, 1974-93 Oscar Blasco, 1986-90 J. R. Blum, 1954-58 R. M. Blumenthal, 1959-68 Colin R. Blyth, 1954-2003 Robert Bohrer, 1971-94 Bela Bollobas, 1979-96 Christer Borell, 1974-96 Jean Bourgain, 1982-2006 (8 folders) Nadjis Bouzar, 1989 J. -
Notices: Highlights
Salt Lake City Meeting (August 5-8)- Page 761 Notices of the American Mathematical Society August 1987, Issue 257 Volume 34, Number 5, Pages 729-872 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings , THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of Notices was sent to the press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change: this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the headquarter's office of the Society. Abstracts of papers to be presented at the meeting must be recejvedat the headquarters of the Society in Providence. Rhode Island. on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information. consult the meeting announcements and the list of organizers of special sessions.