Freeman J. Dyson

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The two-player Iterated Prisoner's Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do(More)
A basic subtlety in the study of statistical mechanics is the following: In nature, we observe abrupt changes in certain basic physical quantities, such as the magnetization of a magnet, but the statistical mechanics of systems with finitely many degrees of freedom is typically real analytic in all external variables. The resolution of this apparent paradox(More)
A simple statistical model is constructed, describing the transition from disorder to order in a population of mutually catalytic molecules undergoing random mutations. The consequences of the model are calculated, and its possible relevance to the problem of the origin of life is discussed. The main conclusion of the analysis is that the model allows(More)
We study the level-spacings distribution for eigenvalues of large N X N matrices from the classical compact groups in the scaling limit when the mean distance between nearest eigenvalues equals 1. Defining by 77N(S) the number of nearest neighbors spacings greater than s > 0 (smaller than s > 0) we prove functional limit theorem for the process(More)
We investigate the fluctuations in Na(R), the number of lattice points n £ Z inside a circle of radius R centered at a fixed point α e [0, I). Assuming that R is smoothly (e.g., uniformly) distributed on a segment 0 ̂ R ^ T9 we prove that the random variable — 7= has a limit distribution as T -> oo (independent of the distribution of R\ which is absolutely(More)