Entropy, Large Deviations, and Statistical Mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1985
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
271 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con verges to zero as n --+ 00, where Sn is the nth partial sum of independent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen tial decay allows one to prove the stronger property of almost sure convergence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly |
| Beschreibung: | 1 Online-Ressource (XIV, 365 p) |
| ISBN: | 9781461385332 9781461385356 |
| DOI: | 10.1007/978-1-4613-8533-2 |
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Datensatz im Suchindex
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| discipline | Mathematik |
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| isbn | 9781461385332 9781461385356 |
| language | English |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Ellis, Richard S. Verfasser aut Entropy, Large Deviations, and Statistical Mechanics by Richard S. Ellis New York, NY Springer New York 1985 1 Online-Ressource (XIV, 365 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 271 This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con verges to zero as n --+ 00, where Sn is the nth partial sum of independent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen tial decay allows one to prove the stronger property of almost sure convergence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly Physics Statistical Physics, Dynamical Systems and Complexity Große Abweichung (DE-588)4330658-5 gnd rswk-swf Entropie (DE-588)4014894-4 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Streuung (DE-588)4058056-8 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s Entropie (DE-588)4014894-4 s Große Abweichung (DE-588)4330658-5 s 1\p DE-604 Wahrscheinlichkeitsmaß (DE-588)4137556-7 s Asymptotik (DE-588)4126634-1 s 2\p DE-604 Streuung (DE-588)4058056-8 s 3\p DE-604 Statistische Thermodynamik (DE-588)4126251-7 s 4\p DE-604 Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 271 (DE-604)BV049758308 271 https://doi.org/10.1007/978-1-4613-8533-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ellis, Richard S. Entropy, Large Deviations, and Statistical Mechanics Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics Physics Statistical Physics, Dynamical Systems and Complexity Große Abweichung (DE-588)4330658-5 gnd Entropie (DE-588)4014894-4 gnd Statistische Mechanik (DE-588)4056999-8 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Streuung (DE-588)4058056-8 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4330658-5 (DE-588)4014894-4 (DE-588)4056999-8 (DE-588)4126251-7 (DE-588)4137556-7 (DE-588)4058056-8 (DE-588)4126634-1 |
| title | Entropy, Large Deviations, and Statistical Mechanics |
| title_auth | Entropy, Large Deviations, and Statistical Mechanics |
| title_exact_search | Entropy, Large Deviations, and Statistical Mechanics |
| title_full | Entropy, Large Deviations, and Statistical Mechanics by Richard S. Ellis |
| title_fullStr | Entropy, Large Deviations, and Statistical Mechanics by Richard S. Ellis |
| title_full_unstemmed | Entropy, Large Deviations, and Statistical Mechanics by Richard S. Ellis |
| title_short | Entropy, Large Deviations, and Statistical Mechanics |
| title_sort | entropy large deviations and statistical mechanics |
| topic | Physics Statistical Physics, Dynamical Systems and Complexity Große Abweichung (DE-588)4330658-5 gnd Entropie (DE-588)4014894-4 gnd Statistische Mechanik (DE-588)4056999-8 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Streuung (DE-588)4058056-8 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Physics Statistical Physics, Dynamical Systems and Complexity Große Abweichung Entropie Statistische Mechanik Statistische Thermodynamik Wahrscheinlichkeitsmaß Streuung Asymptotik |
| url | https://doi.org/10.1007/978-1-4613-8533-2 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT ellisrichards entropylargedeviationsandstatisticalmechanics |