Related papers: Aging uncoupled continuous time random walk limits
We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal…
We report new results related to the two-time dynamics of the coordinate of a quantum free particle, damped through its interaction with a fractal thermal bath (non-ohmic coupling $\sim\omega^\delta$ with $0<\delta<1$ or $1<\delta<2)$. When…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
The SUE machine is used to extend by a factor of 1000 the time-scale of previous studies of the aging, out-of-equilibrium dynamics of the Edwards-Anderson model with binary couplings, on large lattices (L=60). The correlation function,…
We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price…
In the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest. Ageing phenomena are observed during this ever-lasting non-equilibrium evolution. A simple instance of such a behaviour is…
Let $\tau = (\tau_i : i \in {\Bbb Z})$ denote i.i.d.~positive random variables with common distribution $F$ and (conditional on $\tau$) let $X = (X_t : t\geq0, X_0=0)$, be a continuous-time simple symmetric random walk on ${\Bbb Z}$ with…
Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow…
Linear theory of stationary response in thermal systems subjected to external perturbations requires to find equilibrium correlation function of the responding system variable in the absence of external perturbations. Studies of the…
We derive an explicit expression for the Fourier-Laplace transform of the two-point distribution function $p(x_1,t_1;x_2,t_2)$ of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single point…
We analyze generalized space-time fractional motions on undirected networks and lattices. The continuous-time random walk (CTRW) approach of Montroll and Weiss is employed to subordinate a space fractional walk to a generalization of the…
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
We define a family of stochastic Loewner evolution-type processes in finitely connected domains, which are called continuous LERW (loop-erased random walk). A continuous LERW describes a random curve in a finitely connected domain that…
In this work, we consider a modification of the usual Branching Random Walk (BRW), where we give certain independent and identically distributed (i.i.d.) displacements to all the particles at the $n$-th generation, which may be different…
Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting…
We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…
We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…