Organizing Committee
Abstract

Since the days of Boltzmann, it has been well accepted that natural phenomena, when described using tools of statistical mechanics, are governed by various "laws of large numbers." For practitioners of the field this usually means that certain empirical means converge to constants when the limit of a large system is taken. However, evidence has been amassed that such laws apply also to geometric features of these systems and, in particular, to many naturally-defined shapes. Earlier examples where such convergence could be proved include certain interacting particle systems, invasion percolation models and spin systems in equilibrium statistical mechanics.

The last decade has seen a true explosion of "limit-shape" results. New tools of combinatorics, random matrices and representation theory have given us new models for which limit shapes can be determined and further studied: dimer models, polymer models, sorting networks, ASEP (asymmetric exclusion processes), sandpile models, bootstrap percolation models, polynuclear growth models, etc. The goal of the workshop is to attempt to confront this "ZOO" of combinatorial examples with older foundational work and develop a better understanding of the general limit shape phenomenon.

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Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, April 13, 2015
TimeEventLocationMaterials
8:30 - 8:55am EDTLimit Shapes Workshop Registration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTThe limit shape of random SU(3) representations - Dan Romik, University of California, Davis11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTStochastic quantum integrable systems - Ivan Corwin, Columbia University11th Floor Lecture Hall
11:30 - 12:15pm EDTSolving interacting particle systems by Fourier-like transforms - Leonid Petrov, University of Virginia11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch   
2:30 - 3:15pm EDTLimit shapes for interacting particle systems and their universal fluctuations - Patrick Ferrari, Rheinische Friedrich-Wilhelms-Universität Bonn11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTLimit shapes in the Schur process - Dan Betea, Université de Paris VI (Pierre et Marie Curie)11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, April 14, 2015
TimeEventLocationMaterials
9:00 - 9:45am EDTCircles in the Sand - Lionel Levine, Cornell University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTTBA - Charles Smart, Cornell University11th Floor Lecture Hall 
11:30 - 12:15pm EDTThe limit shape of the Abelian Sandpile identity - Andrea Sportiello, Université de Paris XIII (Paris-Nord), CNRS and LIPN11th Floor Lecture Hall
12:30 - 2:00pm EDTBreak for Lunch   
2:00 - 2:45pm EDTSmall-particle limits in a regularized Laplacian random growth model - Amanda Turner, University of Lancaster11th Floor Lecture Hall
2:50 - 3:15pm EDTSIR epidemics on random graphs with a given degree sequence - Malwina Luczak, Queen Mary University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break1th Floor Collaborative Space 
4:00 - 4:25pm EDTThe Shape of Ice - Kari Eloranta, Aalto University11th Floor Lecture Hall
4:30 - 4:55pm EDTPerfect sampling algorithm for Schur processes - Mirjana Vuletic, University of Massachusetts11th Floor Lecture Hall
Wednesday, April 15, 2015
TimeEventLocationMaterials
9:00 - 9:45am EDTAn effective model of facets formation. - Dimitry Ioffe, Technion-Israel Institute of Technology11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTAsymptotic 'inner shape' of a deformed gradient Gibbs field. - Roman Kotecky, University of Warwick11th Floor Lecture Hall
11:30 - 12:15pm EDTHeight fluctuations in interacting dimers - Fabio Toninelli, Université Claude-Bernard (Lyon I)11th Floor Lecture Hall
12:30 - 12:40pm EDTGroup Photo in Lecture Hall11th Floor Lecture Hall 
12:40 - 2:00pm EDTBreak for Lunch   
2:00 - 2:25pm EDTPlane partitions with 2-periodic weights - Sevak Mkrtchyan, University of Rochester11th Floor Lecture Hall
2:30 - 2:55pm EDTThe full extremal process of the discrete Gaussian free field in 2D. - Oren Louidor, Technion-Israel Institute of Technology11th Floor Lecture Hall
3:00 - 4:15pm EDTPoster Session and Coffee/Tea Break11th Floor Lecture Hall and Collaborative Space 
Thursday, April 16, 2015
TimeEventLocationMaterials
9:00 - 9:45am EDTRandom Walk in a one-dimensional Levy random environment - Alessandra Bianchi, Università di Padova11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTMetastability and interface motion in disordered media - Thierry Bodineau, École Polytechnique11th Floor Lecture Hall
11:30 - 12:15pm EDTSubgaussian Rates of Convergence in First Passage Percolation - Ken Alexander, University of Southern California11th Floor Lecture Hall
12:30 - 2:00pm EDTBreak for Lunch   
2:00 - 2:25pm EDTThe Greedy Independent Set in a Random Graph with Given Degrees - Graham Brightwell, London School of Economics and Political Science11th Floor Lecture Hall 
2:30 - 3:15pm EDTGradient Gibbs measures with disorder - Codina Cotar, University College London11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTCentral Limit Theorem for discrete log-gases - Vadim Gorin, Massachusetts Institute of Technology11th Floor Lecture Hall
Friday, April 17, 2015
TimeEventLocationMaterials
9:00 - 9:45am EDTShape theorems in percolation and random walks - Eviatar Procaccia, University of California, Los Angeles11th Floor Lecture Hall 
10:00 - 10:45am EDTStatistical mechanics via asymptotics of symmetric functions - Greta Panova, University of Pennsylvania11th Floor Lecture Hall
10:45 - 11:15am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:15 - 12:00pm EDTThe Z-invariant massive Laplacian on isoradial graphs. - Beatrice deTiliere, Université de Paris VI (Pierre et Marie Curie)11th Floor Lecture Hall 
12:15 - 1:00pm EDTArctic curves for the-six vertex model on generic domains - Filippo Colomo, National Institute of Nuclear Physics (INFN)11th Floor Lecture Hall
1:00 - 2:30pm EDTBreak for Lunch   
2:30 - 2:55pm EDTMinimum mean weighted cycles on randomly weighted graphs. - David Wilson, Microsoft Research11th Floor Lecture Hall 
3:00 - 5:00pm EDTDiscussion11th Floor Lecture Hall and Collaborative Space 
3:00 - 5:00pm EDTDiscussion11th Floor Lecture Hall and Collaborative Space 

Associated Semester Workshops

Phase Transitions and Emergent Properties
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Statistical Mechanics and Combinatorics (ongoing semester course)
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Crystals, Quasicrystals and Random Networks
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Lecture Videos

Arctic curves for the-six vertex model on generic domains

Filippo Colomo
National Institute of Nuclear Physics (INFN)
April 17, 2015

Statistical mechanics via asymptotics of symmetric functions

Greta Panova
University of Pennsylvania
April 17, 2015

Shape theorems in percolation and random walks

Eviatar Procaccia
University of California, Los Angeles
April 17, 2015

Central Limit Theorem for discrete log-gases

Vadim Gorin
Massachusetts Institute of Technology
April 16, 2015

Subgaussian Rates of Convergence in First Passage Percolation

Ken Alexander
University of Southern California
April 16, 2015

Metastability and interface motion in disordered media

Thierry Bodineau
École Polytechnique
April 16, 2015

Random Walk in a one-dimensional Levy random environment

Alessandra Bianchi
Universitá di Padova
April 16, 2015

Plane partitions with 2-periodic weights

Sevak Mkrtchyan
University of Rochester
April 15, 2015

Asymptotic 'inner shape' of a deformed gradient Gibbs field

Roman Kotecky
University of Warwick
April 15, 2015

An effective model of facets formation

Dima Ioffe
Technion-Israel Institute of Technology
April 15, 2015

Perfect sampling algorithm for Schur processes

Mirjana Vuletic
University of Massachusetts
April 14, 2015

The Shape of Ice

Kari Eloranta
Aalto University
April 14, 2015

SIR epidemics on random graphs with a given degree sequence

Malwina Luczak
Queen Mary University
April 14, 2015

The limit shape of the Abelian Sandpile identity

Andrea Sportiello
Université de Paris XIII (Paris-Nord), CNRS and LIPN
April 14, 2015

Limit shapes in the Schur process

Dan Betea
Université de Paris VI (Pierre et Marie Curie)
April 13, 2015

Limit shapes for interacting particle systems and their universal fluctuations

Patrick Ferrari
Rheinische Friedrich-Wilhelms-Universität Bonn
April 13, 2015

Solving interacting particle systems by Fourier-like transforms

Leonid Petrov
University of Virginia
April 13, 2015

Stochastic quantum integrable systems

Ivan Corwin
Columbia University
April 13, 2015