Related papers: Computing stationary probability distributions and…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
In this paper, we study the discrete-time quantum walks on 1D Chain with the moving and swapping shift operators. We derive analytical solutions for the eigenvalues and eigenstates of the evolution operator $\hat{U}$ using the Chebyshev…
Statistics of molecular random walks in a fluid is considered with the help of Bogolyubov equation for generating functional of distribution functions. An invariance group of this equation is found. It results in many exact relations…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its…
The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
We first establish new local limit estimates for the probability that a nondecreasing integer-valued random walk lies at time $n$ at an arbitrary value, encompassing in particular large deviation regimes. This enables us to derive scaling…
To what extent is the underlying distribution of a finitely supported unbiased random walk on $\mathbb{Z}$ determined by the sequence of times at which the walk returns to the origin? The main result of this paper is that, in various…
We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at Level 2.5 for the joint probability of…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…
The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…
We study the asymptotic behaviour of the probability that a weighted sum of centered i.i.d. random variables X_k does not exceed a constant barrier. For regular random walks, the results follow easily from classical fluctuation theory,…
In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…