"This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15-19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics." -- Prové de l'editor

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lgrsnf/N:\!genesis_\0day\springer\10.1007%2F978-3-030-15338-0.pdf

nexusstc/Probability and Analysis in Interacting Physical Systems: In Honor of S.R.S. Varadhan, Berlin, August, 2016/5495cb62f13fa4fa9732ddeb1504d577.pdf

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zlib/no-category/Peter Friz, Wolfgang König, Chiranjib Mukherjee, Stefano Olla/Probability and Analysis in Interacting Physical Systems: In Honor of S.R.S. Varadhan, Berlin, August, 2016_5243374.pdf

475765_1_En_Print.indd

Peter K Friz; Wolfgang König; Chiranjib Mukherjee; Stefano Olla; S. R. S Varadhan

Friz, Peter; König, Wolfgang; Mukherjee, Chiranjib; Olla, Stefano

0007855

Springer Nature Switzerland AG

Springer proceedings in mathematics & statistics, volume 283, Cham, Switzerland, 2019

Springer proceedings in mathematics & statistics, 1st ed. 2019, Cham, 2019

Springer proceedings in mathematics et statistics, volume 283, Cham, 2019

Springer Proceedings in Mathematics & Statistics 283, 1st ed., 2019

Springer Nature, Cham, 2019

Switzerland, Switzerland

1, 20190524

sm75863943

producers:
Acrobat Distiller 10.0.0 (Windows)

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Preface 8
List of Participants of the workshop at TU Berlin, 15–19 August 2016 11
Contents 14
Yang–Mills for Probabilists 15
1 Introduction 15
2 Euclidean Yang–Mills Theories 17
3 Lattice Gauge Theories 18
4 Wilson Loop Variables and Quark Confinement 21
5 The Problem of Defining the Continuum Limit 23
6 Review of the Mathematical Literature 25
References 27
Multiscale Systems, Homogenization, and Rough Paths 31
1 Introduction 32
2 Emergence of Randomness in Deterministic Dynamical Systems 34
2.1 The Weak Invariance Principle 34
2.2 First Applications to Fast-Slow Systems 36
2.3 Chaotic Dynamics: CLT and the WIP 37
3 General Rough Path Theory 45
3.1 Limit Theorems from Rough Path Analysis 45
3.2 WIPs in Rough Path Theory 49
4 Applications to Fast-Slow Systems 51
4.1 Chaotic Dynamics: Enhanced WIP and Moments 51
4.2 Continuous Dynamics 54
4.3 Discrete Dynamics 56
5 Extension to Families and Non-product Case 57
References 59
The Deterministic and Stochastic Shallow Lake Problem 63
1 Introduction 64
2 The General Setting and the Main Results 66
3 The Proof of Proposition 1 68
4 Viscosity Solutions and the Hamilton–Jacobi–Bellman Equation 78
5 A Numerical Scheme and Optimal Dynamics 83
References 87
Independent Particles in a Dynamical Random Environment 89
1 Introduction and Results 90
1.1 The Particle Process and Its Invariant Distributions 91
1.2 Limit of the Current Process 95
2 Coupled Process 99
3 Invariant Measures 102
3.1 Proof of Uniqueness 110
4 Covariances of the Invariant Measures 113
5 Convergence of Centered Current Fluctuations 120
6 The Quenched Mean Process 128
References 134
Stable Limit Laws for Reaction-Diffusion in Random Environment 136
1 Introduction 137
2 Notations and Results 139
3 Rank-One Perturbation for Schrödinger Operators 144
3.1 Principal Eigenvalue and Eigenfunction 144
3.2 Green Function of the Unperturbed Operator 145
3.3 Proof of Theorem 4 147
4 High Peak Statistics of a Weibull Potential 148
5 Stable Limit Laws and Structure of the Scaling 149
5.1 Existence of the Scaling Function 149
5.2 Properties of the Scaling Function 150
6 Convergence to Stable Laws 153
6.1 Mesoscopic Scales 153
6.2 Dirichlet Boundary Conditions 154
6.3 Criteria for Convergence to Stable Laws 155
6.4 Lévy-Khintchine Spectral Function 157
6.5 The Truncated Moments 163
6.6 The Parameters of the Infinite Divisible Law 165
6.7 Conclusion 166
7 Annealed Asymptotics 166
7.1 Preliminary Estimates 167
7.2 Path Decomposition of Annealed First Moment 168
7.3 Asymptotic Lower Bound 169
7.4 Asymptotic Upper Bound 171
7.5 Proof of Proposition 2 172
8 Asymptotic Expansion of the Scaling Function for 1<ρ<(3+sqrt17)/2 173
References 184
Quenched Central Limit Theorem for the Stochastic Heat Equation in Weak Disorder 185
1 Introduction and the Result 185
1.1 Motivation 185
1.2 The Result 186
2 Proof of Theorem 1.1 192
References 200
GOE and Airy2to1 Marginal Distribution via Symplectic Schur Functions 202
1 Introduction 202
2 From Determinants to Fredholm Determinants 207
3 Steepest Descent Analysis 210
4 Point-to-Line Last Passage Percolation and GOE 215
5 Point-to-Half-Line Last Passage Percolation and Airy2to1 220
References 223
A Large Deviations Principle for the Polar Empirical Measure in the Two-Dimensional Symmetric Simple Exclusion Process 225
1 Introduction 225
2 Notation and Results 226
3 Superexponential Estimate 231
4 Energy Estimate 237
5 Energy and Rate Function Iα 240
6 The Upper Bound 243
7 The lower bound 250
References 252
On the Growth of a Superlinear Preferential Attachment Scheme 253
1 Model and Results 253
1.1 Results 256
2 Proofs 258
2.1 Martingale Decompositions 258
2.2 Leading Order Asymptotics of Zk(n),S(n) and V(n) 262
2.3 Refined Asymptotics and Fluctuations for Zk(n) 271
References 274
A Natural Probabilistic Model on the Integers and Its Relation to Dickman-Type Distributions and Buchstab's Function 276
1 Introduction and Statement of Results 277
2 Proof of Proposition 3 288
3 If the Limiting Distribution Exists, It Must Be Dickman 289
4 Proof of Theorem 1.1 290
5 Proof of Theorem 1.2 293
6 Proof of Theorem 1.3 293
References 302

Front Matter ....Pages i-xv
Yang–Mills for Probabilists (Sourav Chatterjee)....Pages 1-16
Multiscale Systems, Homogenization, and Rough Paths (Ilya Chevyrev, Peter K. Friz, Alexey Korepanov, Ian Melbourne, Huilin Zhang)....Pages 17-48
The Deterministic and Stochastic Shallow Lake Problem (G. T. Kossioris, M. Loulakis, P. E. Souganidis)....Pages 49-74
Independent Particles in a Dynamical Random Environment (Mathew Joseph, Firas Rassoul-Agha, Timo Seppäläinen)....Pages 75-121
Stable Limit Laws for Reaction-Diffusion in Random Environment (Gérard Ben Arous, Stanislav Molchanov, Alejandro F. Ramírez)....Pages 123-171
Quenched Central Limit Theorem for the Stochastic Heat Equation in Weak Disorder (Yannic Bröker, Chiranjib Mukherjee)....Pages 173-189
GOE and \({\mathrm{Airy}}_{2\rightarrow 1}\) Marginal Distribution via Symplectic Schur Functions (Elia Bisi, Nikos Zygouras)....Pages 191-213
A Large Deviations Principle for the Polar Empirical Measure in the Two-Dimensional Symmetric Simple Exclusion Process (Claudio Landim, Chih-Chung Chang, Tzong-Yow Lee)....Pages 215-242
On the Growth of a Superlinear Preferential Attachment Scheme (Sunder Sethuraman, Shankar C. Venkataramani)....Pages 243-265
A Natural Probabilistic Model on the Integers and Its Relation to Dickman-Type Distributions and Buchstab’s Function (Ross G. Pinsky)....Pages 267-294

"This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15-19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics"--Page 4 of cover

This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15{u2013}19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics

2019-05-26