Disorder and Critical Phenomena Through Basic Probability Models École d’Été de Probabilités de Saint-Flour XL – 2010 /

• Main Author: Giacomin, Giambattista (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes in Mathematics, 2025
• Subjects: Mathematics.; Applied mathematics.; Engineering mathematics.; Probabilities.; Physics.; Statistical physics.; Dynamical systems.; Probability Theory and Stochastic Processes.; Applications of Mathematics.; Statistical Physics, Dynamical Systems and Complexity.; Mathematical Methods in Physics.

Understanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aimi...

Table of Contents:

• 1 Introduction
• 2 Homogeneous pinning systems: a class of exactly solved models
• 3 Introduction to disordered pinning models
• 4 Irrelevant disorder estimates
• 5 Relevant disorder estimates: the smoothing phenomenon
• 6 Critical point shift: the fractional moment method
• 7 The coarse graining procedure
• 8 Path properties.