Ebook: Probability in Complex Physical Systems: In Honour of Erwin Bolthausen and Jürgen Gärtner

Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.

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Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and J?rgen G?rtner, whose scientific work has profoundly influenced the field and all of the present contributions.

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Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and J?rgen G?rtner, whose scientific work has profoundly influenced the field and all of the present contributions.

Content:
Front Matter....Pages i-xix
Front Matter....Pages 11-11
Laudatio: The Mathematical Work of J?rgen G?rtner....Pages 1-10
Front Matter....Pages 11-11
The Parabolic Anderson Model with Long Range Basic Hamiltonian and Weibull Type Random Potential....Pages 13-31
Parabolic Anderson Model with Voter Catalysts: Dichotomy in the Behavior of Lyapunov Exponents....Pages 33-68
Precise Asymptotics for the Parabolic Anderson Model with a Moving Catalyst or Trap....Pages 69-89
Parabolic Anderson Model with a Finite Number of Moving Catalysts....Pages 91-117
Survival Probability of a Random Walk Among a Poisson System of Moving Traps....Pages 119-158
Quenched Lyapunov Exponent for the Parabolic Anderson Model in a Dynamic Random Environment....Pages 159-193
Asymptotic Shape and Propagation of Fronts for Growth Models in Dynamic Random Environment....Pages 195-223
The Parabolic Anderson Model with Acceleration and Deceleration....Pages 225-245
A Scaling Limit Theorem for the Parabolic Anderson Model with Exponential Potential....Pages 247-272
Front Matter....Pages 273-273
The Strong Interaction Limit of Continuous-Time Weakly Self-Avoiding Walk....Pages 275-287
Copolymers at Selective Interfaces: Settled Issues and Open Problems....Pages 289-311
Some Locally Self-Interacting Walks on the Integers....Pages 313-338
Stretched Polymers in Random Environment....Pages 339-369
Front Matter....Pages 371-371
Multiscale Analysis: Fisher–Wright Diffusions with Rare Mutations and Selection, Logistic Branching System....Pages 373-408
Properties of States of Super-?-Stable Motion with Branching of Index 1 + ?....Pages 409-421
Front Matter....Pages 423-423
A Quenched Large Deviation Principle and a Parisi Formula for a Perceptron Version of the GREM....Pages 425-442
Metastability: From Mean Field Models to SPDEs....Pages 443-462
Hydrodynamic Limit for the ?? Interface Model via Two-Scale Approach....Pages 463-490
Statistical Mechanics on Isoradial Graphs....Pages 491-512

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Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and J?rgen G?rtner, whose scientific work has profoundly influenced the field and all of the present contributions.

Content:
Front Matter....Pages i-xix
Front Matter....Pages 11-11
Laudatio: The Mathematical Work of J?rgen G?rtner....Pages 1-10
Front Matter....Pages 11-11
The Parabolic Anderson Model with Long Range Basic Hamiltonian and Weibull Type Random Potential....Pages 13-31
Parabolic Anderson Model with Voter Catalysts: Dichotomy in the Behavior of Lyapunov Exponents....Pages 33-68
Precise Asymptotics for the Parabolic Anderson Model with a Moving Catalyst or Trap....Pages 69-89
Parabolic Anderson Model with a Finite Number of Moving Catalysts....Pages 91-117
Survival Probability of a Random Walk Among a Poisson System of Moving Traps....Pages 119-158
Quenched Lyapunov Exponent for the Parabolic Anderson Model in a Dynamic Random Environment....Pages 159-193
Asymptotic Shape and Propagation of Fronts for Growth Models in Dynamic Random Environment....Pages 195-223
The Parabolic Anderson Model with Acceleration and Deceleration....Pages 225-245
A Scaling Limit Theorem for the Parabolic Anderson Model with Exponential Potential....Pages 247-272
Front Matter....Pages 273-273
The Strong Interaction Limit of Continuous-Time Weakly Self-Avoiding Walk....Pages 275-287
Copolymers at Selective Interfaces: Settled Issues and Open Problems....Pages 289-311
Some Locally Self-Interacting Walks on the Integers....Pages 313-338
Stretched Polymers in Random Environment....Pages 339-369
Front Matter....Pages 371-371
Multiscale Analysis: Fisher–Wright Diffusions with Rare Mutations and Selection, Logistic Branching System....Pages 373-408
Properties of States of Super-?-Stable Motion with Branching of Index 1 + ?....Pages 409-421
Front Matter....Pages 423-423
A Quenched Large Deviation Principle and a Parisi Formula for a Perceptron Version of the GREM....Pages 425-442
Metastability: From Mean Field Models to SPDEs....Pages 443-462
Hydrodynamic Limit for the ?? Interface Model via Two-Scale Approach....Pages 463-490
Statistical Mechanics on Isoradial Graphs....Pages 491-512
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