1307.7903 (Satoru Morita et al.)

Analytical solution of stochastic model of risk-spreading with global
coupling    [PDF]

Satoru Morita, Jin Yoshimura

We study a stochastic matrix model to understand the mechanics of risk-spreading (i.e., bet-hedging) by dispersion. We obtained an analytical solution in the high-dimensional case of global coupling. The result shows that optimal dispersion leads to Zipf's law. Moreover, we found that the arithmetic average of the long-term growth rate converges to the geometric one, because the sample size is finite.

View original: http://arxiv.org/abs/1307.7903