159 research outputs found
Parity and Ruin in a Stochastic Game
We study an elementary two-player card game where in each round players
compare cards and the holder of the smallest card wins. Using the rate
equations approach, we treat the stochastic version of the game in which cards
are drawn randomly. We obtain an exact solution for arbitrary initial
conditions. In general, the game approaches a steady state where the card
densities of the two players are proportional to each other. The leading small
size behavior of the initial card densities determines the corresponding
proportionality constant, while the next correction governs the asymptotic time
dependence. The relaxation towards the steady state exhibits a rich behavior,
e.g., it may be algebraically slow or exponentially fast. Moreover, in ruin
situations where one player eventually wins all cards, the game may even end in
a finite time.Comment: 4 pages, 1 figur
Domain Number Distribution in the Nonequilibrium Ising Model
We study domain distributions in the one-dimensional Ising model subject to
zero-temperature Glauber and Kawasaki dynamics. The survival probability of a
domain, , and an unreacted domain, , are characterized by two independent nontrivial exponents. We
develop an independent interval approximation that provides close estimates for
many characteristics of the domain length and number distributions including
the scaling exponents.Comment: 9 pages, 4 figures, revte
- …