說明 
v, 118 pages : illustrations ; 26 cm 

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volume nc rdacarrier 
系列 
Memoirs of the American Mathematical Society, 00659266 ; number 1222


Memoirs of the American Mathematical Society ; no. 1222

附註 
"September 2018, volume 255, number 1222 (fifth of 7 numbers)." 

Includes bibliographical references 

Introduction  Statement of results  Proof of theorem 2.1  Proof of theorem 2.3  Asymptotic analysis of Kn and Rn  Proof of proposition 2.4  Proof of lemma 4.3  Random initial points  Proof of theorem 2.6: the general case 

"In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with [lower case 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. 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 (sineuniversality 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."Publisher's website 
主題 
Brownian motion processes


Mesoscopic phenomena (Physics)


Stochastic differential equations


Stochastic processes

Alt Author 
Johansson, Kurt, 1960 author

