We study the expected distance of a two-dimensional walk in the plane with unit steps in random directions. A series evaluation and recursions are obtained making it possible to explicitly formulate this distance for small number of steps. Closed form expressions for all the moments of a 2-step and a 3-step walk are given, and a formula is conjectured for the 4-step walk. Heavy use is made of t...

The Brownian loop soup introduced in [3] is a Poissonian realization from a σ-finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Komlós, M...

in this paper we focus on the tracking performance of incremental adaptive LMS algorithm in an adaptive network. For this reason we consider the unknown weight vector to be a time varying sequence. First we analyze the performance of network in tracking a time varying weight vector and then we explain the estimation of Rayleigh fading channel through a random walk model. Closed form relations a...

Impairments in cell migration processes may cause various diseases, among which cancer cell metastasis, tumor angiogenesis, and the disability of immune cells to infiltrate into tumors are prominent ones. Mathematical modeling has been widely used to analyze the cell migration process. Cell migration is a complicated process and requires statistical methods such as random walk for proper analys...

In this paper I work out the rate of convergence of a non-symmetric random walk on the dicyclic group (Dicn) and that of its symmetric analogue on the same group. The analysis is via group representation techniques from Diaconis (1988) and closely follows the analysis of random walk on cyclic group in Chapter 3C of Diaconis. I find that while the mixing times (the time for the random walk to ge...