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Book
ISBN: 9781470429645 1470429640 Year: 2018 Publisher: Providence, RI : American Mathematical Society,
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Brownian motion processes. --- Mesoscopic phenomena (Physics) --- Stochastic differential equations. --- Stochastic processes. --- Processus de mouvement brownien --- Systèmes mésoscopiques --- Équations différentielles stochastiques --- Processus stochastiques --- Mouvement brownien, Processus de --- Mouvement brownien, Processus de. --- Systèmes mésoscopiques. --- Équations différentielles stochastiques. --- Processus stochastiques.
Book
ISBN: 1470448211 Year: 2018 Publisher: Providence, Rhode Island : American Mathematical Society,
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In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with eta =2. Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.
Book
ISBN: 9780821869284 Year: 2012 Publisher: Providence, R.I. American Mathematical Society
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Boundary value problems. --- Hermitian structures. --- Eigenvalues. --- Random matrices. --- Problèmes aux limites --- Structures hermitiennes --- Valeurs propres --- Matrices aléatoires --- 51 <082.1> --- Mathematics--Series --- Problèmes aux limites --- Matrices aléatoires --- Ordered algebraic structures --- Boundary value problems --- Eigenvalues --- Hermitian structures --- Random matrices --- Matrices, Random --- Matrices --- Structures, Hermitian --- Complex manifolds --- Geometry, Differential --- Kählerian structures --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems
Dissertation
Year: 2008 Publisher: Leuven K.U.Leuven. Faculteit Wetenschappen
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