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Entropy, Large Deviations, and Statistical Mechanics: 271 (Die Grundlehren der Mathematischen Wissenschaften) - Tapa dura
Sinopsis
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 indepen- dent 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 conver- gence (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.
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Reseña del editor
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 indepen dent 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 conver gence (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.
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Entropy, Large Deviations, and Statistical Mechanics
Librería: Better World Books, Mishawaka, IN, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
Condición: Good. Former library book; may include library markings. Used book that is in clean, average condition without any missing pages. Nº de ref. del artículo: GRP99067413
Cantidad disponible: 1 disponibles
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Entropy, Large Deviations, and Statistical Mechanics
Publicado por
Springer-Verlag, New York, NY, 1985
ISBN 10: 038796052X
ISBN 13: 9780387960524
Antiguo o usado
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Original o primera edición
Librería: Black Cat Hill Books, Oregon City, OR, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
Hardcover. Condición: Near Fine. First Edition; First Printing. Near Fine: The Book shows mild shelving wear to the lower extremities and even milder wear to the upper corner tips; sun-blanching to the yellow background field of the rear panel (the black titles thereon remain bold and clearly legible) ; the binding is square and secure; the text is clean. Free of creased or dog-eared pages in the text. Free of any underlining, hi-lighting or marginalia or marks in the text. Free of ownership names, dates, addresses, notations, inscriptions, stamps, or labels. A handsome copy, structurally sound and tightly bound, showing mild wear and a single cosmetic imperfection. No DJ as issued. NOT a Remainder, Book-Club, or Ex-Library. Large 8vo (9.5 x 6.35 x 0.9 inches). Language: English. Weight: 25 ounces. Hardcover: No DJ as issued. 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. 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. ; Grundlehren Der Mathematischen Wissenschaften: a Series of Comprehensive Studies in Mathematics; Vol. 271; Large 8vo 9" - 10" tall; xiv, 364 pages. Nº de ref. del artículo: 59381
Cantidad disponible: 1 disponibles