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REM Universality for Random Hamiltonians
We survey in this paper a universality phenomenon which shows that some characteristics of complex random energy landscapes are model-independent, or...
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Linear and sub-linear growth and the CLT for hitting times of a random walk in random environment on a strip
The main goal of this work is to study the asymptotic behaviour of hitting times of a random walk (RW) in a quenched random environment (RE) on a...
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Simple transient random walks in one-dimensional random environment: the central limit theorem
We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide...
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Cugliandolo-Kurchan equations for dynamics of Spin-Glasses
We study the Langevin dynamics for the family of spherical p -spin disordered mean-field models of statistical physics. We prove that in the limit of...
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Phase transition and critical behavior in a model of organized criticality
We study a model of ‘‘organized’’ criticality, where a single avalanche propagates through an a priori static (i.e., organized) sandpile...
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Large deviations and mean-field theory for asymmetric random recurrent neural networks
In this article, we study the asymptotic dynamics of a noisy discrete time neural network, with random asymmetric couplings and thresholds. More...
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Large deviations for random walks on Galton–Watson trees: averaging and uncertainty
In the study of large deviations for random walks in random environment, a key distinction has emerged between quenched asymptotics, conditional on...
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Diffusive scaling of the spectral gap for the dilute Ising lattice-gas dynamics below the percolation threshold
We consider a conservative stochastic lattice-gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on ℤ ...
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Aging of spherical spin glasses
Sompolinski and Zippelius (1981) propose the study of dynamical systems whose invariant measures are the Gibbs measures for (hard to analyze)...
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Almost sure asymptotics for the continuous parabolic Anderson model
We consider the parabolic Anderson problem ∂ t u = κΔ u + ξ( x ) u on ℝ + ×ℝ d with initial condition u (0, x ) = 1. Here κ > 0 is a diffusion constant and ξ...
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Metastability in stochastic dynamics of disordered mean-field models
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures....
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Quenched, annealed and functional large deviations for one-dimensional random walk in random environment
Suppose that the integers are assigned random variables { ω i } (taking values in the unit interval), which serve as an environment. This environment...
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Correlation structure of intermittency in the parabolic Anderson model
Consider the Cauchy problem ∂ u ( x, t )/∂ t = ℋ u ( x, t ) ( x ∈ℤ d , t ≥ 0) with initial condition u ( x , 0) ≡ 1 and with ℋ the Anderson Hamiltonian ℋ = κΔ + ξ....
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Precise large deviation estimates for a one-dimensional random walk in a random environment
} (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk { X k } (called a RWRE) which, when...
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Parabolic problems for the Anderson model
This is a continuation of our previous work [6] on the investigation of intermittency for the parabolic equation (∂/∂ t ) u =H u on ℝ + ×ℤ d associated with...
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Averaged and quenched propagation of chaos for spin glass dynamics
We study the asymptotic behaviour for both asymmetric and symmetric spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by...
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Sanov results for Glauber spin-glass dynamics
In this paper we prove a Sanov result, i.e. a Large Deviation Principle ( LDP ) for the distribution of the empirical measure, for the annealed Glauber...
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Large deviations for Langevin spin glass dynamics
We study the asymptotic behaviour of asymmetrical spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We...