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作者 Duits, Maurice, author
書名 On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / Maurice Duits, Kurt Johansson
出版項 Providence, RI : American Mathematical Society, [2018]
國際標準書號 9781470429645
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA274.75 D85 2018    在架上    30340200561268
說明 v, 118 pages : illustrations ; 26 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Memoirs of the American Mathematical Society, 0065-9266 ; 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 (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."--Publisher's website
主題 Brownian motion processes
Mesoscopic phenomena (Physics)
Stochastic differential equations
Stochastic processes
Alt Author Johansson, Kurt, 1960- author
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