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On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / / Maurice Duits, Kurt Johansson
| On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / / Maurice Duits, Kurt Johansson |
| Autore | Duits Maurice |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (130 pages) |
| Disciplina | 519.2/33 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Stochastic processes
Stochastic differential equations Mesoscopic phenomena (Physics) Brownian motion processes |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-4821-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Statement of results -- 2.1. Assumptions on ⱼ⁽ⁿ⁾ -- 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 _{ } and _{ }^{ } -- 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 _{ } and _{ } -- 5.1. Integrable form of _{ } -- 5.2. The functions ℰⱼ -- 5.3. Saddle points -- 5.4. Deforming the contours -- 5.5. Asymptotics for ⱼ and ⱼ -- 5.6. Proof of Lemma 3.2 -- 5.7. Asymptotics for _{ }( , ) -- 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 logaritmic 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 -- 7.2. Estimating _{ }^{ _{ }^{\eps}} -- 7.3. Estimating _{ }^{ _{ }^{\eps}} -- 7.4. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1/2 -- 7.5. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1 -- Chapter 8. Random initial points -- 8.1. Preliminary lemmas -- 8.2. Regularity of the initial points -- 8.3. Smoothening the test function -- 8.4. Approximating _{ }( ) -- 8.5. Proof of Theorem 2.5, and Theorem 2.6 with the assumption ₀( )≠0 -- Chapter 9. Proof of Theorem 2.6: the general case -- 9.1. Smoothening of the test function -- 9.2. Change of variables -- 9.3. Expansion into moments.
9.4. Proof of Proposition 9.1 -- 9.5. Proof of Theorem 2.6: the general case -- Appendix -- Bibliography -- Back Cover. |
| Record Nr. | UNINA-9910478891903321 |
Duits Maurice
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / / Maurice Duits, Kurt Johansson
| On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / / Maurice Duits, Kurt Johansson |
| Autore | Duits Maurice |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (130 pages) |
| Disciplina | 530.475 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Brownian motion processes |
| ISBN | 1-4704-4821-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Statement of results -- 2.1. Assumptions on ⱼ⁽ⁿ⁾ -- 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 _{ } and _{ }^{ } -- 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 _{ } and _{ } -- 5.1. Integrable form of _{ } -- 5.2. The functions ℰⱼ -- 5.3. Saddle points -- 5.4. Deforming the contours -- 5.5. Asymptotics for ⱼ and ⱼ -- 5.6. Proof of Lemma 3.2 -- 5.7. Asymptotics for _{ }( , ) -- 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 logaritmic 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 -- 7.2. Estimating _{ }^{ _{ }^{\eps}} -- 7.3. Estimating _{ }^{ _{ }^{\eps}} -- 7.4. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1/2 -- 7.5. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1 -- Chapter 8. Random initial points -- 8.1. Preliminary lemmas -- 8.2. Regularity of the initial points -- 8.3. Smoothening the test function -- 8.4. Approximating _{ }( ) -- 8.5. Proof of Theorem 2.5, and Theorem 2.6 with the assumption ₀( )≠0 -- Chapter 9. Proof of Theorem 2.6: the general case -- 9.1. Smoothening of the test function -- 9.2. Change of variables -- 9.3. Expansion into moments.
9.4. Proof of Proposition 9.1 -- 9.5. Proof of Theorem 2.6: the general case -- Appendix -- Bibliography -- Back Cover. |
| Record Nr. | UNINA-9910793296403321 |
|
Duits Maurice
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / / Maurice Duits, Kurt Johansson
| On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / / Maurice Duits, Kurt Johansson |
| Autore | Duits Maurice |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (130 pages) |
| Disciplina | 530.475 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Brownian motion processes |
| ISBN | 1-4704-4821-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Statement of results -- 2.1. Assumptions on ⱼ⁽ⁿ⁾ -- 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 _{ } and _{ }^{ } -- 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 _{ } and _{ } -- 5.1. Integrable form of _{ } -- 5.2. The functions ℰⱼ -- 5.3. Saddle points -- 5.4. Deforming the contours -- 5.5. Asymptotics for ⱼ and ⱼ -- 5.6. Proof of Lemma 3.2 -- 5.7. Asymptotics for _{ }( , ) -- 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 logaritmic 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 -- 7.2. Estimating _{ }^{ _{ }^{\eps}} -- 7.3. Estimating _{ }^{ _{ }^{\eps}} -- 7.4. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1/2 -- 7.5. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1 -- Chapter 8. Random initial points -- 8.1. Preliminary lemmas -- 8.2. Regularity of the initial points -- 8.3. Smoothening the test function -- 8.4. Approximating _{ }( ) -- 8.5. Proof of Theorem 2.5, and Theorem 2.6 with the assumption ₀( )≠0 -- Chapter 9. Proof of Theorem 2.6: the general case -- 9.1. Smoothening of the test function -- 9.2. Change of variables -- 9.3. Expansion into moments.
9.4. Proof of Proposition 9.1 -- 9.5. Proof of Theorem 2.6: the general case -- Appendix -- Bibliography -- Back Cover. |
| Record Nr. | UNINA-9910813200903321 |
|
Duits Maurice
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||