Directed Polymers in Random Environments École d'Été de Probabilités de Saint-Flour XLVI – 2016 /

• Main Author: Comets, Francis (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Lecture Notes in Mathematics, 2175
• Subjects: Mathematics.; Probabilities.; Probability Theory and Stochastic Processes.; Statistical Physics and Dynamical Systems.

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main question is: What does the path of a random walk look like if rewards and penalties are spatial...

Table of Contents:

• 1 Introduction
• 2 Thermodynamics and Phase Transition
• 3 The martingale approach and the L2 region
• 4 Lattice versus tree
• 5 Semimartingale approach and localization transition
• 6 Log-Gamma polymer model
• 7 Kardar-Parisi-Zhang equation and universality
• 8 Variational formulas.