Topics in Contemporary Probability and Its Applications

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CRC Press, 18.04.1995 - 400 Seiten
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Probability theory has grown from a modest study of simple games of change to a subject with application in almost every branch of knowledge and science. In this exciting book, a number of distinguished probabilists discuss their current work and applications in an easily understood manner. Chapters show that new directions in probability have been suggested by the application of probability to other fields and other disciplines of mathematics. The study of polymer chains in chemistry led to the study of self-avoiding random walks; the study of the Ising model in physics and models for epidemics in biology led to the study of the probability theory of interacting particle systems. The stochastic calculus has allowed probabilists to solve problems in classical analysis, in theory of investment, and in engineering. The mathematical formulation of game theory has led to new insights into decisions under uncertainty. These new developments in probability are vividly illustrated throughout the book.
 

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Inhalt

Uniform Random Spanning Trees
1
Simple and SelfAvoiding
55
Some Connections Between Brownian Motion and Analysis
75
Can You Feel the Shape of a Manifold With Brownian Motion?
89
Some New Games For Your Computer
103
some larger experiments David Griffeath
113
References
114
Problems For Students of Probability
117
Characteristics of directed graphs useful for a measurement and theory
238
Models
240
Connections
241
Basic properties of the heterogeneous cascade model for finites
243
Limit theory of the linear cascade model for large S
247
Dynamics of food webs
251
References
257
How Many Times Should You Shuffle a Deck of Cards?
261

Systems and deterministic case
119
Measures
124
Random systems
128
Proofs of ergodicity and fast convergence
134
Percolation systems
137
Nonergodicity and slow convergence
140
Standard votings
147
Onedimensional conservators
149
Chaos approximation
153
References
154
MetropolisType Monte Carlo Simulation Algorithms and Simulated Annealing
159
Metropolistype Monte Carlo simulation algorithms
164
Simulated annealing
197
References
225
Random Graphs in Ecology
233
What is a shuffle really?
262
The riffle shuffle
265
How far away from randomness?
268
Rising sequences
269
flshuffles
270
Virtues of the ashuffle
271
Putting it all together
275
The inverse shuffle
277
Another approach to sufficient shuffling
279
Stochastic Games and Operators
291
The Bandit Model For Decision Processes
321
Three Bewitching Paradoxes
355
Index
371
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