相关论文: Aging Random Walks
Renewal process is a point process where an inter-event time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the…
Many recent experiments probed the off equilibrium dynamics of spin glasses and other glassy systems through temperature cycling protocols and observed memory and rejuvenation phenomena. Here we show through numerical simulations, using…
We propose a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is sampled at time zero only; (II) the random environment is resampled at every…
We present some simple computer simulations that indicate that at short time aging is realized in a simple model of binary glasses. It is interesting to note that modest computer simulations are enough to evidenziate this effect. We also…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
The twin paradox of the special theory of relativity has given rise to a large body of literature discussing its implications. In its standard form, the traveler changes velocity only at the destination of the trip, so that he appears to…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has considerably grown recently thanks to the discovery that the trap like aging…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
We propose a statistical model of a large random network with high connectivity in order to describe the behavior of {\it E.\,coli} cells after exposure to acute stress. The building blocks of this network are feedback cycles typical of the…
We use confocal microscopy to directly visualize the dynamics of aging colloidal glasses. We prepare a colloidal suspension at high density, a simple model system which shares many properties with other glasses, and initiate experiments by…
Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with…
We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First, we establish that if…
The GREM-like trap model is a continuous time Markov jump process on the leaves of a finite volume $L$-level tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural…
We study the Metropolis dynamics of the simplest mean-field spin glass model, the Random Energy Model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a…
We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time…
Using RG we investigate the non-equilibrium relaxation of the (Cardy-Ostlund) 2D random Sine-Gordon model, which describes pinned arrays of lines. Its statics exhibits a marginal ($\theta=0$) glass phase for $T<T_g$ described by a line of…
We are interested in the out of equilibrium phenomena observed in the electrical conductance of disordered insulators at low temperature, which may be signatures of the electron coulomb glass state. The present work is devoted to the…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…