相关论文: The area of exponential random walk and partial su…

We consider a d-dimensional random walk in random scenery X(n), where the scenery consists of i.i.d. with exponential moments but a tail decay of the form exp(-c t^a) with a<d/2. We study the probability, when averaged over both randomness,…

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…

An ordinal pattern for a finite sequence of real numbers is a permutation that records the relative positions in the sequence. For random walks with steps drawn uniformly from $[-1,1]$, we show an ordinal pattern occurs with probability…

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…

We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…

Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is…

We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $0<b<1$, with each turn. This process generates a random probability measure on $\R$, that is, the limit of uniform distribution among the $2^n$…

We investigate the statistics of the convex hull for a single run-and-tumble particle in two dimensions. Run-and-tumble particle, also known as persistent random walker, has gained significant interest in the recent years due to its…

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…

Let $S_k$ be a random walk in $R^d$ such that its distribution of increments does not assign mass to hyperplanes. We study the probability $p_n$ that the convex hull $conv (S_1, \ldots , S_n)$ of the first $n$ steps of the walk does not…

In this article, we first give a comprehensive description of random walk (RW) problem focusing on self-similarity, dynamic scaling and its connection to diffusion phenomena. One of the main goals of our work is to check how robust the RW…

We determine, to within O(1), the expected minimal position at level n in certain branching random walks. The walks under consideration have displacement vector (v_1,v_2,...), where each v_j is the sum of j independent Exponential(1) random…

The Pairwise Einstein Model (PEM) of steps not only justifies the use of the Generalized Wigner Distribution (GWD) for Terrace Width Distributions (TWDs), it also predicts a specific form for the Step Position Distribution (SPD), i.e., the…

We obtain the joint distribution $P_N (X, K|Z)$ of the location $X$ of a one-dimensional symmetric next neighbor random walk on the integer lattice, and the number of times the walk has visited a specified site $Z$. This distribution has a…

We study the statistical properties of the area and the absolute area under the trajectories of subdiffusive random walks. Using different frameworks to describe subdiffusion (as the scaled Brownian motion, fractional Brownian motion, the…

We consider a random walk $(Z^{(1)}_n, ..., Z^{(K+1)}_n) \in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a…

A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of the current position. We explicitly identify an invariant…

Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that their distributions…

We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the…

We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the record of an individual random walk with the…