Topics in Contemporary Probability and Its Applications
CRC Press, 18.04.1995 - 400 Seiten
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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Uniform Random Spanning Trees
Simple and SelfAvoiding
Some Connections Between Brownian Motion and Analysis
Can You Feel the Shape of a Manifold With Brownian Motion?
Some New Games For Your Computer
some larger experiments David Griffeath
Problems For Students of Probability
Characteristics of directed graphs useful for a measurement and theory
Basic properties of the heterogeneous cascade model for finites
Limit theory of the linear cascade model for large S
Dynamics of food webs
How Many Times Should You Shuffle a Deck of Cards?
Systems and deterministic case
Proofs of ergodicity and fast convergence
Nonergodicity and slow convergence
MetropolisType Monte Carlo Simulation Algorithms and Simulated Annealing
Metropolistype Monte Carlo simulation algorithms
Random Graphs in Ecology
What is a shuffle really?
The riffle shuffle
How far away from randomness?
Virtues of the ashuffle
Putting it all together
The inverse shuffle
Another approach to sufficient shuffling
Stochastic Games and Operators
The Bandit Model For Decision Processes
Three Bewitching Paradoxes
1-armed bandit a-shuffle algorithms assume asymptotic attractors bounded Brownian motion calculate called cards cascade model cellular automata choose Cohen conditional probability configuration constant convergence corresponding cut and interleaving deck defined denote density deterministic system distribution dynamics edge eigenvalue equal equation ergodic example Exercise expected number exponent FIGURE finite food webs formula function Gibbs sampler Gittins index given global hence independent infinite initial integer interactions irreducible Lemma limit linear LVCM Markov chain mathematical matrix measure Monte Carlo neighbors node number of species operator optimal packet paths percolation permutation play player problem proof Prove random system random variables random walk result Riemannian manifold riffle shuffle rising sequences satisfies self-adjoint self-avoiding walk simple random walk simulated annealing space stochastic game strategy subsection Suppose Theorem theory transition probability uniform spanning tree variation distance vector vertex vertices voltage zero