Related papers: Convergence of clock processes in random environme…

Applying the new tools developed in [G1], we investigate the arcsine aging regime of the random hopping time dynamics of the REM. Our results are optimal in several ways. They cover the full time-scale and temperature domain where this…

We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law…

Using a method developed by Durrett and Resnick [22] we establish general criteria for the convergence of properly rescaled clock processes of random dynamics in random environments on infinite graphs. This complements the results of [26],…

We consider a version of a Glauber dynamics for a p-spin Sherrington--Kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the N-dimensional hypercube. We show that, for any p>2 and any inverse…

We study the aging behavior of the Random Energy Model (REM) evolving under Metropolis dynamics. We prove that a classical two-time correlation function converges almost surely to the arcsine law distribution function that characterizes…

We consider Random Hopping Time (RHT) dynamics of the Sherrington - Kirkpatrick (SK) model and p-spin models of spin glasses. For any of these models and for any inverse temperature we prove that, on time scales that are sub-exponential in…

This paper extends recent results on aging in mean field spin glasses on short time scales, obtained by Ben Arous and Gun [2] in law with respect to the environment, to results that hold almost surely, respectively in probability, with…

In this paper the celebrated arcsine aging scheme of G. Ben Arous and J. Cern\'y is taken up. Using a brand new approach based on point processes and weak convergence techniques, this scheme is implemented in a wide class of Markov…

We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…

We give a general proof of aging for trap models using the arcsine law for stable subordinators. This proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape. We…

In the seminal work [5], Ben Arous and \v{C}ern\'y give a general characterization of aging for trap models in terms of $\alpha$-stable subordinators with $\alpha \in (0,1)$. Some of the important examples that fall into this universality…

A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…

In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…

We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky features, reflecting or absorbing boundaries and…

In 1979 Penrose hypothesized that the arrows of time are explained by the hypothesis that the fundamental laws are time irreversible. That is, our reversible laws, such as the standard model and general relativity are effective, and emerge…

We provide a set of conditions which ensure the almost sure convergence of a class of simulated annealing algorithms on a bounded set $\mathcal{X}\subset\mathbb{R}^d$ based on a time-varying Markov kernel. The class of algorithms considered…

We study the rate of convergence to equilibrium of the self-repellent random walk and its local time process on the discrete circle $\mathbb{Z}_n$. While the self-repellent random walk alone is non-Markovian since the jump rates depend on…

We prove that the Arcsine law as the time-averaged distribution for classical harmonic oscillators emerges from the distributions for quantum harmonic oscillators in terms of noncommutative algebraic probability. This is nothing but a…

We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…

In this paper, we introduce the concept of random time changes in dynamical systems. The sub- ordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…