Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain

The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good agreement with numerical simulations. These first order results do not depend on the irrational incommensurability.Comment: 10 Pages in RevTeX, 2 Postscript figure

Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions

We address the thermodynamics (equilibrium density profiles, phase diagram, instability analysis...) and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, we derive the analytic form of the density scaling profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max} is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in the limit of large D. Finally, we solve the problem in D=2, which displays rather rich and peculiar features

Universal statistical properties of poker tournaments

We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament

Growth rate for the expected value of a generalized random Fibonacci sequence

A random Fibonacci sequence is defined by the relation g_n = | g_{n-1} +/- g_{n-2} |, where the +/- sign is chosen by tossing a balanced coin for each n. We generalize these sequences to the case when the coin is unbalanced (denoting by p the probability of a +), and the recurrence relation is of the form g_n = |\lambda g_{n-1} +/- g_{n-2} |. When \lambda >=2 and 0 < p <= 1, we prove that the expected value of g_n grows exponentially fast. When \lambda = \lambda_k = 2 cos(\pi/k) for some fixed integer k>2, we show that the expected value of g_n grows exponentially fast for p>(2-\lambda_k)/4 and give an algebraic expression for the growth rate. The involved methods extend (and correct) those introduced in a previous paper by the second author

Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape

A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The statistics of the number of changes of the dominant genotype from a finite set of genotypes are exactly obtained confirming existing conjectures based on numerics.Comment: 5 pages RevTex 2 figures .ep

Anomalous Drude Model

A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long tail and even a non-vanishing first moment. The collision averaged motion is either regular diffusive or L\'evy-flight like. The anomalous diffusion coefficients show complex scaling laws. The conductivity can be calculated in the diffusive regime. The model is of interest for the phenomenological study of electronic transport in quasicrystals.Comment: 4 pages, latex, 2 figures, to be published in Physical Review Letter

A phason disordered two dimensional quantum antiferromagnet

We examine a novel type of disorder in quantum antiferromagnets. Our model consists of localized spins with antiferromagnetic exchanges on a bipartite quasiperiodic structure, which is geometrically disordered in such a way that no frustration is introduced. In the limit of zero disorder, the structure is the perfect Penrose rhombus tiling. This tiling is progressively disordered by augmenting the number of random "phason flips" or local tile-reshuffling operations. The ground state remains N\'eel ordered, and we have studied its properties as a function of increasing disorder using linear spin wave theory and quantum Monte Carlo. We find that the ground state energy decreases, indicating enhanced quantum fluctuations with increasing disorder. The magnon spectrum is progressively smoothed, and the effective spin wave velocity of low energy magnons increases with disorder. For large disorder, the ground state energy as well as the average staggered magnetization tend towards limiting values characteristic of this type of randomized tilings.Comment: 5 pages, 7 figure

Undestanding Baseball Team Standings and Streaks

Can one understand the statistics of wins and losses of baseball teams? Are their consecutive-game winning and losing streaks self-reinforcing or can they be described statistically? We apply the Bradley-Terry model, which incorporates the heterogeneity of team strengths in a minimalist way, to answer these questions. Excellent agreement is found between the predictions of the Bradley-Terry model and the rank dependence of the average number team wins and losses in major-league baseball over the past century when the distribution of team strengths is taken to be uniformly distributed over a finite range. Using this uniform strength distribution, we also find very good agreement between model predictions and the observed distribution of consecutive-game team winning and losing streaks over the last half-century; however, the agreement is less good for the previous half-century. The behavior of the last half-century supports the hypothesis that long streaks are primarily statistical in origin with little self-reinforcing component. The data further show that the past half-century of baseball has been more competitive than the preceding half-century.Comment: 5 pages, 6 figures, 2-column revtex4 format; version 2: considerably expanded to 9 pages with 8 figure