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- William H. Press, Freeman J. Dyson
- Proceedings of the National Academy of Sciences…
- 2012

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)

holds. He was thus led to conjecture the existence of some other partition statistic (which he called the crank); this unknown statistic should provide a combinatorial interpretation of ^-p(lln + 6) in the same way that (1.1) and (1.2) treat the primes 5 and 7. In [4, 5], one of us was able to find a crank relative to vector partitions as follows: For a… (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)

- Freeman J. Dyson
- Journal of Molecular Evolution
- 1982

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)

- Freeman J. Dyson
- 1998

- Freeman J. Dyson
- J. Comb. Theory, Ser. A
- 1989

- Alexander Soshnikov, Freeman J. Dyson, +6 authors Fieeman J. Dyson
- 2009

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)

- Freeman J. Dyson
- Science
- 1960

If extraterrestrial intelligent beings exist and have reached a high level of technical development, one by-product of their energy metabolism is likely to be the large-scale conversion of starlight into far-infrared radiation. It is proposed that a search for sources of infrared radiation should accompany the recently initiated search for interstellar… (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)

We consider random non-hermitean matrices in the large N limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitean random matrices, in contrast to hermitean random matrices. To overcome this difficulty, we show that associated to each ensemble of nonhermitean matrices there is an auxiliary ensemble of random… (More)