2007

Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams

Alain Comtet 1, 2, Satya N. Majumdar 1, Stephane Ouvry 1, Sanjib Sabhapandit 1 Journal of statistical mechanics-theory and experiment (2007) P10001 We compute the limit shapes of the Young diagrams of the minimal difference $p$ partitions and provide a simple physical interpretation for the limit shapes. We also calculate the asymptotic distribution of the largest part of the Young diagram and show that

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Inferring periodic orbits from spectra of simple shaped micro-lasers

Mélanie Lebental 1, 2, Nadia Djellali 1, Carole Arnaud 1, Jean-Sébastien Lauret 1, Joseph Zyss 1, R. Dubertrand 2, C. Schmit 2, E. Bogomolny 2 Physical Review A: Atomic, Molecular and Optical Physics 76 (2007) 023830 Dielectric micro-cavities are widely used as laser resonators and characterizations of their spectra are of interest for various applications. We experimentally investigate micro-lasers of simple shapes (Fabry-Perot, square, pentagon, and disk). Their lasing spectra consist mainly

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Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems

Florent Krzakala 1, Andrea Montanari 2, Federico Ricci-Tersenghi, Guilhem Semerjian 2, Lenka Zdeborova 3 Proceeding of the national academy of sciences 104, 25 (2007) 10318 An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and q-coloring of random regular

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General flux to a trap in one and three dimensions

Robert M. Ziff 1, Satya N. Majumdar 2, Alain Comtet 2, 3 Journal of Physics: Condensed Matter 19 (2007) 065102 The problem of the flux to a spherical trap in one and three dimensions, for diffusing particles undergoing discrete-time jumps with a given radial probability distribution, is solved in general, verifying the Smoluchowski-like solution in which the effective trap radius is reduced

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Fractional Laplacian in Bounded Domains

A. Zoia 1, A. Rosso 2, 3, M. Kardar 3 Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 021116 The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on

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