On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion /

"In this paper we study mesoscopic fluctuations for Dyson's Brownian motion with [beta] = 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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Duits, Maurice (Autor), Johansson, Kurt, 1960- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, 2018.
Colección:Memoirs of the American Mathematical Society ; no. 1222.
Temas:
Brownian motion processes.
Mesoscopic phenomena (Physics)
Stochastic differential equations.
Stochastic processes.
Stochastic Processes
Processus de mouvement brownien.
Systèmes mésoscopiques.
Équations différentielles stochastiques.
Processus stochastiques.
MATHEMATICS > Applied.
MATHEMATICS > Probability & Statistics > General.
Procesos estocásticos
Probabilidades
Ecuaciones diferenciales estocásticas
Movimientos brownianos
Brownian motion processes
Stochastic differential equations
Stochastic processes
Acceso en línea:Texto completo
Descripción
Sumario:"In this paper we study mesoscopic fluctuations for Dyson's Brownian motion with [beta] = 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. In this paper we investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that we consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but we have not yet reached equilibrium at the macrosopic scale. We describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. We consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, we obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE."--Page v
Notas:"September 2018, Volume 255, Number 1222 (fifth of 7 numbers)."
Descripción Física:1 online resource (v, 118 pages : illustrations
Bibliografía:Includes bibliographical references.
ISBN:1470448211
9781470448219
ISSN:0065-9266 ;

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