title: Analytical solution of a stochastic model of risk spreading with global coupling.
abstract: We study a stochastic matrix model to understand the mechanics of risk spreading (or bet hedging) by dispersion. Up to now, this model has been mostly dealt with numerically, except for the well-mixed case. Here, we present an analytical result that shows that optimal dispersion leads to Zipf's law. Moreover, we found that the arithmetic ensemble average of the total growth rate converges to the geometric one, because the sample size is finite.
authors: Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
authors: Satoru
authors: S
authors: Morita
authors: Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan and Marine Biosystems Research Center, Chiba University, Uchiura, Kamogawa, Chiba 299-5502, Japan.
authors: Jin
authors: J
authors: Yoshimura