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Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

Pierpaolo Vivo 1, Satya N. Majumdar 2, Oriol Bohigas 2 Journal of Physics A: Mathematical and General 40 (2007) 4317-4337 We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x […]

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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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