Related papers: Global random walk for one-dimensional one-phase S…

This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…

We study nearest neighbor random walks on fixed environments of $\mathbb{Z}$ composed of two point types : $(1/2,1/2)$ and $(p,1-p)$ for $p>1/2$. We show that for every environment with density of $p$ drifts bounded by $\lambda$ we have…

We describe the full exit boundary of random walks on homogeneous trees, in particular, on the free groups. This model exhibits a phase transition, namely, the family of Markov measures under study loses ergodicity as a parameter of the…

In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the…

We introduce via perturbation a class of random walks in reversible dynamic environments having a spectral gap. In this setting one can apply the mathematical results derived in http://arxiv.org/abs/1602.06322. As first results, we show…

We study the transmission of random walkers through a finite-size inhomogeneous material with a quenched, long-range correlated distribution of scatterers. We focus on a finite one-dimensional structure where walkers undergo random…

We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to…

We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…

Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…

Stochastic resetting -- the intermittent restart of random processes -- has profoundly reshaped first-passage theory, providing a mechanism to control and optimize completion times. While the influence of resetting on mean first-passage…

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to…

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…

A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…

A one phase Stefan problem in nonlinear conduction is considered. The problem is shown to admit a unique solution for small times. An exact solution is obtained which is a travelling front moving with constant speed.

Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting…

We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…

An excited random walk is a non-Markovian extension of the simple random walk, in which the walk's behavior at time $n$ is impacted by the path it has taken up to time $n$. The properties of an excited random walk are more difficult to…

It is well known that the spectral form factor (SFF) of a possibly degenerate many-body Hamiltonian can be identified with a planar random walk taking steps of unequal length. In this paper we push this identification further and propose to…

Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…