On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
September 2018
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 255, number 1222 (fifth of 7 numbers) |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | v, 118, 4 ungezählte Seiten |
| ISBN: | 9781470429645 |
Internformat
MARC
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| 100 | 1 | |a Duits, Maurice |d 1980- |0 (DE-588)1022344803 |4 aut | |
| 245 | 1 | 0 | |a On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion |c Maurice Duits, Kurt Johansson |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c September 2018 | |
| 264 | 4 | |c © 2018 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 255, number 1222 (fifth of 7 numbers) | |
| 700 | 1 | |a Johansson, Kurt |4 aut | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v volume 255, number 1222 (fifth of 7 numbers) |w (DE-604)BV008000141 |9 1222 | |
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Datensatz im Suchindex
| _version_ | 1804179055438725120 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction
Chapter 2. Statement of results
2.1. Assumptions on
2.2. Deterministic initial points
2.3. Concentration inequalities
2.4. Random initial points
2.5. Further remarks
2.6. Overview of the rest of the paper
Chapter 3. Proof of Theorem 2.1
3.1. Determinantal strucure
3.2. Asymptotic results for Kn and R£
3.3. Proof of Theorem 2.1
Chapter 4. Proof of Theorem 2.3
4.1. Overview of the proof
4.2. The loop equations
4.3. Loop equations on the mesoscopic scale
4.4. Proof of Theorem 2.3
Chapter 5. Asymptotic analysis of Kn and Rn
5.1. Integrable form of Kn
5.2. The functions £j
5.3. Saddle points
5.4. Deforming the contours
5.5. Asymptotics for j)j and tpj
5.6. Proof of Lemma 3.2
5.7. Asymptotics for Kn(x,x)
5.8. Asymptotics for
Chapter 6. Proof of Proposition 2.4
6.1. Preliminaries
6.2. A first concentration inequality
6.3. Proof of Poposition 6.2
6.4. A concentration inequality using the logaritrnic Sobolev inequality
6.5. Proof of Proposition 2.4
6.6. One more concentration inequality
Chapter 7. Proof of Lemma 4.3
7.1. Preliminaries
iii
1
5
5
6
9
10
13
14
15
15
16
18
21
21
22
24
25
29
29
31
32
36
39
42
44
45
53
53
54
58
61
62
65
67
67
IV
CONTENTS
7.2.
7.3.
7.4.
7.5.
Estimating Anfa
Estimating Bn*a
Estimating C^a
Estimating C^a
for 0 a. 1/2
for 0 a 1
69
70
72
74
Chapter 8. Random initial points 79
8.1. Preliminary lemmas 79
8.2. Regularity of the initial points 82
8.3. Smoothening the test function 84
8.4. Approximating Un(z) 86
8.5. Proof of Theorem 2.5, and Theorem 2.6 with the assumption po(/) ^0 94
Chapter 9. Proof of Theorem 2.6: the general case 97
9.1. Smoothening of the test function 97
9.2. Change of variables 98
9.3. Expansion into moments 104
9.4. Proof of Proposition 9.1 106
9.5. Proof of Theorem 2.6: the general case 110
113
Appendix
Bibliography
117
|
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| author | Duits, Maurice 1980- Johansson, Kurt |
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| indexdate | 2024-07-10T08:13:47Z |
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| isbn | 9781470429645 |
| language | English |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Duits, Maurice 1980- (DE-588)1022344803 aut On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion Maurice Duits, Kurt Johansson Providence, Rhode Island American Mathematical Society September 2018 © 2018 v, 118, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 255, number 1222 (fifth of 7 numbers) Johansson, Kurt aut Memoirs of the American Mathematical Society volume 255, number 1222 (fifth of 7 numbers) (DE-604)BV008000141 1222 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030668829&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duits, Maurice 1980- Johansson, Kurt On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion Memoirs of the American Mathematical Society |
| title | On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion |
| title_auth | On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion |
| title_exact_search | On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion |
| title_full | On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion Maurice Duits, Kurt Johansson |
| title_fullStr | On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion Maurice Duits, Kurt Johansson |
| title_full_unstemmed | On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion Maurice Duits, Kurt Johansson |
| title_short | On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion |
| title_sort | on mesoscopic equilibrium for linear statistics in dyson s brownian motion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030668829&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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