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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2018.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1222. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 001 | EBOOKCENTRAL_on1054216569 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
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| 008 | 180925s2018 riua ob 000 0 eng | ||
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| 020 | |a 1470448211 |q (online) | ||
| 020 | |a 9781470448219 |q (electronic bk.) | ||
| 020 | |z 9781470429645 |q (alk. paper) | ||
| 020 | |z 1470429640 |q (alk. paper) | ||
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| 035 | |a (OCoLC)1054216569 | ||
| 050 | 4 | |a QA274.75 |b .D85 2018 | |
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| 049 | |a UAMI | ||
| 100 | 1 | |a Duits, Maurice, |e author. | |
| 245 | 1 | 0 | |a On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / |c Maurice Duits, Kurt Johansson. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c 2018. | |
| 300 | |a 1 online resource (v, 118 pages : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 255, number 1222 | |
| 500 | |a "September 2018, Volume 255, Number 1222 (fifth of 7 numbers)." | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a 1. Introduction -- 2. Statement of results -- 3. Proof of Theorem 2.1 -- 4. Proof of Theorem 2.3 -- 5. Asymptotic analysis of Kn and Rn -- 6. Proof of Proposition 2.4 -- 7. Proof of Lemma 4.3 -- 8. Random initial points -- 9. Proof of Theorem 2.6: the general case. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a "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 | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Brownian motion processes. | |
| 650 | 0 | |a Mesoscopic phenomena (Physics) | |
| 650 | 0 | |a Stochastic differential equations. | |
| 650 | 0 | |a Stochastic processes. | |
| 650 | 2 | |a Stochastic Processes | |
| 650 | 6 | |a Processus de mouvement brownien. | |
| 650 | 6 | |a Systèmes mésoscopiques. | |
| 650 | 6 | |a Équations différentielles stochastiques. | |
| 650 | 6 | |a Processus stochastiques. | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Procesos estocásticos |2 embne | |
| 650 | 7 | |a Probabilidades |2 embne | |
| 650 | 0 | 7 | |a Ecuaciones diferenciales estocásticas |2 embucm |
| 650 | 0 | 7 | |a Movimientos brownianos |2 embucm |
| 650 | 7 | |a Brownian motion processes |2 fast | |
| 650 | 7 | |a Mesoscopic phenomena (Physics) |2 fast | |
| 650 | 7 | |a Stochastic differential equations |2 fast | |
| 650 | 7 | |a Stochastic processes |2 fast | |
| 700 | 1 | |a Johansson, Kurt, |d 1960- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJppFqjcmVY7pwMfmq6Myd | |
| 758 | |i has work: |a On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGR9K4tyTtqQyJgJh7gyv3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Duits, Maurice. |t On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion. |d Providence, RI : American Mathematical Society, [2018] |z 1470429640 |z 9781470429645 |w (DLC) 2018040867 |w (OCoLC)1039625485 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1222. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5571104 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5571104 | ||
| 938 | |a EBSCOhost |b EBSC |n 1924189 | ||
| 938 | |a YBP Library Services |b YANK |n 15817154 | ||
| 994 | |a 92 |b IZTAP | ||