Poincaré cycle of a multibox Ehrenfest urn model with directed transport

Distributions, continued fractions, and the Ehrenfest Urn model

A Central Limit Property under a Modified Ehrenfest Urn Design

We consider a stochastic process in a modified Ehrenfest urn model. The modification prescribes there to be a minimum number of balls in each urn, and the process records the differences between treatment assignments under a sampling scheme implemented with this modified Ehrenfest urn model. In contrast to the result that the difference process forms a Markov chain and converges to a stationary...

Ehrenfest urn revisited: playing the game on a realistic fluid model.

The Ehrenfest urn process, also known as the dogs and fleas model, is realistically simulated by molecular dynamics of the Lennard-Jones fluid. The key variable is Delta(z) -i.e., the absolute value of the difference between the number of particles in one half of the simulation box and in the other half. This is a pure-jump stochastic process induced, under coarse graining, by the deterministic...

Reversing the drift of the Ehrenfest urn model and three conditionings

We consider a drift-reversed version of the celebrated Ehrenfest urn process with N balls. For this ‘dual’ process, the boundaries are assumed to be absorbing and so the killing times at the boundaries play a central role. Three natural conditionings on the fixation/extinction events pertaining to this model are investigated. Some spectral informations on the conditioned Markoff chains are obta...

Phases in the Mixing of Gases via the Ehrenfest Urn Model

The Ehrenfest urn is a model for the mixing of gases in two chambers. Classic research deals with this system as a Markovian model with a fixed number of balls, and derives the steady-state behavior as a binomial distribution (which can be approximated by a normal distribution). We study the gradual change for an urn containing n balls from the initial condition to the steady state. We look at ...