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math.PR2007★ 9 cited
Clustering in a stochastic model of one-dimensional gas
Vladislav V. Vysotsky
We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of identical particles that are randomly distributed…
math.PR2006
A functional limit theorem for the position of a particle in a Lorentz type model
Vladislav Vysotsky
Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R^d. The particle is accelerated by a constant external field; wh…
math.PR2006
The area of exponential random walk and partial sums of uniform order statistics
Vladislav Vysotsky
Let S_i be a random walk with standard exponential increments. We call \sum_{i=1}^k S_i its k-step area. The random variable V = \inf_{k \ge 1} \frac{2}{k(k+1)} \sum_{i=1}^k S_i pl…