Dynamics of trap models

Abstract

These notes cover one of the topics of the class given in the Les Houches Summer School ``Mathematical statistical physics'' in July 2005. The lectures tried to give a summary of the recent mathematical results about the long-time behaviour of dynamics of (mean-field) spin-glasses and other disordered media. We have chosen here to restrict the scope of these notes to the dynamics of trap models only, but to cover this topic in somewhat more depth.

Lecture Notes for Les Houches Summer School "Mathematical statistical physics", 52 pages

References in corpus (9)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Models of traps and glass phenomenology
• Multiple scaling regimes in simple aging models
• Aging in the random energy model
• Hopping in the Glass Configuration Space: Subaging and Generalized Scaling Laws
• Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit
• Aging and spin-glass dynamics
• Aging properties of Sinai's model of random walk in random environment
• Glauber Dynamics and Ageing

Cited by in corpus (19)

• Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential
• Scaling limit for trap models on ${\mathbb{Z}}^d$
• Statistical mechanics of a single particle in a multiscale random potential: Parisi landscapes in finite dimensional Euclidean spaces
• Multifractality and Freezing Phenomena in Random Energy Landscapes: an Introduction
• A polymer in a multi-interface medium
• Universality and extremal aging for dynamics of spin glasses on sub-exponential time scales
• Localisation in the Bouchaud-Anderson Model
• Scaling limits and aging for asymmetric trap models on the complete graph and K-processes
• Trap models with vanishing drift: Scaling limits and aging regimes
• Differentiability of the speed of biased random walks on Galton-Watson trees
• Anomalous scaling regime for one-dimensional Mott variable-range hopping
• Non-Gaussian fluctuations of randomly trapped random walks
• Local times of subdiffusive biased walks on trees
• Spectral analysis of 1D nearest-neighbor random walks and applications to subdiffusive trap and barrier models
• Quenched scaling limits of trap models
• Functional limit theorems for the Bouchaud trap model with slowly varying traps
• Tunneling of the Kawasaki dynamics at low temperatures in two dimensions
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
• Biased random walk on critical Galton-Watson trees conditioned to survive