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.

Confirmed Speakers & Participants

Workshop Schedule

Monday, April 13, 2015
TimeEventLocationMaterials
8:30 - 8:55Limit Shapes Workshop Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45The limit shape of random SU(3) representations - Dan Romik, University of California, Davis11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Stochastic quantum integrable systems - Ivan Corwin, Columbia University11th Floor Lecture Hall
11:30 - 12:15Solving interacting particle systems by Fourier-like transforms - Leonid Petrov, University of Virginia11th Floor Lecture Hall
12:30 - 2:30Break for Lunch   
2:30 - 3:15Limit shapes for interacting particle systems and their universal fluctuations - Patrick Ferrari, Rheinische Friedrich-Wilhelms-Universität Bonn11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Limit shapes in the Schur process - Dan Betea, Université de Paris VI (Pierre et Marie Curie)11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, April 14, 2015
TimeEventLocationMaterials
9:00 - 9:45Circles in the Sand - Lionel Levine, Cornell University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15TBA - Charles Smart, Cornell University11th Floor Lecture Hall 
11:30 - 12:15The limit shape of the Abelian Sandpile identity - Andrea Sportiello, Université de Paris XIII (Paris-Nord), CNRS and LIPN11th Floor Lecture Hall
12:30 - 2:00Break for Lunch   
2:00 - 2:45Small-particle limits in a regularized Laplacian random growth model - Amanda Turner, University of Lancaster11th Floor Lecture Hall
2:50 - 3:15SIR epidemics on random graphs with a given degree sequence - Malwina Luczak, Queen Mary University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break1th Floor Collaborative Space 
4:00 - 4:25The Shape of Ice - Kari Eloranta, Aalto University11th Floor Lecture Hall
4:30 - 4:55Perfect sampling algorithm for Schur processes - Mirjana Vuletic, University of Massachusetts11th Floor Lecture Hall
Wednesday, April 15, 2015
TimeEventLocationMaterials
9:00 - 9:45An effective model of facets formation. - Dimitry Ioffe, Technion-Israel Institute of Technology11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Asymptotic 'inner shape' of a deformed gradient Gibbs field. - Roman Kotecky, University of Warwick11th Floor Lecture Hall
11:30 - 12:15Height fluctuations in interacting dimers - Fabio Toninelli, Université Claude-Bernard (Lyon I)11th Floor Lecture Hall
12:30 - 12:40Group Photo in Lecture Hall11th Floor Lecture Hall 
12:40 - 2:00Break for Lunch   
2:00 - 2:25Plane partitions with 2-periodic weights - Sevak Mkrtchyan, University of Rochester11th Floor Lecture Hall
2:30 - 2:55The full extremal process of the discrete Gaussian free field in 2D. - Oren Louidor, Technion-Israel Institute of Technology11th Floor Lecture Hall
3:00 - 4:15Poster Session and Coffee/Tea Break11th Floor Lecture Hall and Collaborative Space 
Thursday, April 16, 2015
TimeEventLocationMaterials
9:00 - 9:45Random Walk in a one-dimensional Levy random environment - Alessandra Bianchi, Università di Padova11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Metastability and interface motion in disordered media - Thierry Bodineau, École Polytechnique11th Floor Lecture Hall
11:30 - 12:15Subgaussian Rates of Convergence in First Passage Percolation - Ken Alexander, University of Southern California11th Floor Lecture Hall
12:30 - 2:00Break for Lunch   
2:00 - 2:25The Greedy Independent Set in a Random Graph with Given Degrees - Graham Brightwell, London School of Economics and Political Science11th Floor Lecture Hall 
2:30 - 3:15Gradient Gibbs measures with disorder - Codina Cotar, University College London11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Central Limit Theorem for discrete log-gases - Vadim Gorin, Massachusetts Institute of Technology11th Floor Lecture Hall
Friday, April 17, 2015
TimeEventLocationMaterials
9:00 - 9:45Shape theorems in percolation and random walks - Eviatar Procaccia, University of California, Los Angeles11th Floor Lecture Hall 
10:00 - 10:45Statistical mechanics via asymptotics of symmetric functions - Greta Panova, University of Pennsylvania11th Floor Lecture Hall
10:45 - 11:15Coffee/Tea Break11th Floor Collaborative Space 
11:15 - 12:00The Z-invariant massive Laplacian on isoradial graphs. - Beatrice deTiliere, Université de Paris VI (Pierre et Marie Curie)11th Floor Lecture Hall 
12:15 - 1:00Arctic curves for the-six vertex model on generic domains - Filippo Colomo, National Institute of Nuclear Physics (INFN)11th Floor Lecture Hall
1:00 - 2:30Break for Lunch   
2:30 - 2:55Minimum mean weighted cycles on randomly weighted graphs. - David Wilson, Microsoft Research11th Floor Lecture Hall 
3:00 - 5:00Discussion11th Floor Lecture Hall and Collaborative Space 
3:00 - 5:00Discussion11th Floor Lecture Hall and Collaborative Space 

Associated Semester Workshops

Phase Transitions and Emergent Properties
Crystals, Quasicrystals and Random Networks

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