Related papers: Dirichlet random walks

Let $(\xi_1, \eta_1)$, $(\xi_2, \eta_2),\ldots$ be independent identically distributed $\mathbb{N}^2$-valued random vectors with arbitrarily dependent components. The sequence $(\Theta_k)_{k\in\mathbb{N}}$ defined by…

The dynamical discrete web (DyDW),introduced in recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter \tau. The evolution is by…

Let $W$ be a finite Weyl group and $\widetilde W$ the corresponding affine Weyl group. A random element of $\widetilde W$ can be obtained as a reduced random walk on the alcoves of $\widetilde W$. By a theorem of Lam (Ann. Prob. 2015), such…

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…

Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…

An important line of research is the investigation of the laws of random variables known as Dirichlet means as discussed in Cifarelli and Regazzini(1990). However there is not much information on inter-relationships between different…

In this paper we study random flights in R^d with displacements possessing Dirichlet distributions of two different types and uniformly oriented. The randomization of the number of displacements has the form of a generalized Poisson process…

We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…

We prove joint functional limit theorems in the Skorokhod space equipped with the $J_1$-topology for successive Lebesgue-Stieltjes convolutions of nondecreasing stochastic processes with themselves. These convolutions arise naturally in…

In this paper, we consider random walk in random environment on $\mathbb{Z}^{d}\,(d\geq1)$ and prove the Strassen's strong invariance principle for this model, via martingale argument and the theory of fractional coboundaries of Derriennic…

We study the distributions of the continuous-time quantum walk on a one-dimensional lattice. In particular we will consider walks on unbounded lattices, walks with one and two boundaries and Dirichlet boundary conditions, and walks with…

Consider $G=SL_2(\mathbb{Z})/\{\pm I\}$ acting on the complex upper half plane $H$ by $h_M(z)=\frac{az+b}{cz+d},$ for $M \in G$. Let $D=\{z \in H: |z|\geq 1, |\Re(z)|\leq 1/2\}$. We consider the set $\mathcal{E} \subset G$ with the $9$…

The generalized Dickman distribution ${\cal D}_\theta$ with parameter $\theta>0$ is the unique solution to the distributional equality $W=_d W^*$, where \begin{eqnarray} W^*=_d U^{1/\theta}(W+1) \qquad (1) \end{eqnarray} with $W$…

A n-step Pearson-Gamma random walk in Rd starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained…

Let $\{\mm_n, n=0,1,...\}$ be the supercritical branching random walk starting with one initial ancestor located at the origin of the real line. For $n=0,1,...$ let $W_n$ be the moment generating function of $\mm_n$ normalized by its mean.…

Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes,…

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic…

We extend our study of random walks and induced Dirichlet forms on self-similar sets [arXiv:1604.05440, 1612.01708] to compact spaces of homogeneous type $(K, \rho ,\mu)$. A successive partition on $K$ brings a natural augmented tree…

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves…

We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ in which the upper triangular entries are independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\mathbb E…