Related papers: Nonintersecting random walks in the neighborhood o…
The continuous-time random walk is defined as a Poissonization of discrete-time random walk. We study the noncolliding system of continuous-time simple and symmetric random walks on ${\mathbb{Z}}$. We show that the system is determinantal…
We consider a process of noncolliding $q$-exchangeable random walks on $\mathbb{Z}$ making steps $0$ (straight) and $-1$ (down). A single random walk is called $q$-exchangeable if under an elementary transposition of the neighboring steps…
We consider the $N$-particle noncolliding Bernoulli random walk --- a discrete time Markov process in $\mathbb{Z}^{N}$ obtained from a collection of $N$ independent simple random walks with steps $\in\{0,1\}$ by conditioning that they never…
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…
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…
Consider $a$ particles performing simple, symmetric, non-intersecting random walks, starting at points $2(j-1)$, $1\le j\le a$ at time 0 and ending at $2(j-1)+c-b$ at time $b+c$. This can also be interpreted as a random rhombus tiling of an…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
We consider random walks on the nonnegative integers in a space-time dependent random environment. We assume that transition probabilities are given by independent $\mathrm{Beta}(\mu,\mu)$ distributed random variables, with a specific…
We consider a discrete-time TASEP, where each particle jumps according to Bernoulli random variables with particle-dependent and time-inhomogeneous parameters. We use the combinatorics of the Robinson-Schensted-Knuth correspondence and…
In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel…
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…
We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to…
For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…
We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…