A Poisson random walk is Bernoulli

A Random Walk with Exponential Travel Times

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

Poisson Approximation for Sums of Dependent Bernoulli Random Variables

In this paper, we use the Stein-Chen method to determine a non-uniform bound for approximating the distribution of sums of dependent Bernoulli random variables by Poisson distribution. We give two formulas of non-uniform bounds and their applications.

Loop-Erased Random Walk and Poisson Kernel on Planar Graphs

Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on Z2 is SLE2. We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs embedded into C so that edges do not cross one another). We show that if the scaling limit of the random walk is planar Brownian motion, then the scaling limit of its loop-erasure is SLE2. Our main co...

What is Quantum Random Walk?

• Classical: random walk in one dimension describes a particle that moves in the positive or negative direction according to the random outcome of some unbiased binary variable (e.g., a fair coin). • Quantum: The particle with two degree of freedom (for example spin) can move left or right according to its spin and one unitary operator can play coin roles (for example Hadamard operator).In quan...

How to Find an Extra Head: Optimal Random Shifts of Bernoulli and Poisson Random Fields