Related papers: Non parametric estimation for random walks in rand…
We study the asymptotic behaviour of random walks in i.i.d. random environments on $\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when…
We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally,…
We obtain an exact formula for the first-passage time probability distribution for random walks on complex networks using inverse Laplace transform. We write the formula as the summation of finitely many terms with different frequencies…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
We present an analytical approximation scheme for the first passage time distribution on a finite interval of a random walker on a random forcing energy landscape. The approximation scheme captures the behavior of the distribution over all…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
Finding a local minimum or maximum of a function is often achieved through the gradient-descent optimization method. For a function in dimension d, the gradient requires to compute at each step d partial derivatives. This method is for…
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…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
We discuss nonparametric estimators of the distribution of the incubation time of a disease. The classical approach in these models is to use parametric families like Weibull, log-normal or gamma in the estimation procedure. We analyze…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…
We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…
Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…
We consider the random walk in an independent and identically distributed (i.i.d.) random environment on a Cayley graph of a finite free product of copies of $\mathbb{Z}$ and $\mathbb{Z}_2$. Such a Cayley graph is readily seen to be a…
We consider a random walk on a homogeneous space $G/\Lambda$ where $G$ is a non-compact simple Lie group and $\Lambda$ is a lattice. The walk is driven by a probability measure $\mu$ on $G$ whose support generates a Zariski-dense subgroup.…