Random Matrix Models and Their Applications
by Pavel Bleher, Alexander Its
Publisher: Cambridge University Press 2001
Number of pages: 438
The book covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems. Its focus on the interaction between physics and mathematics will make it a welcome addition to the shelves of graduate students and researchers in both fields, as will its expository emphasis.
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by Marcus Kracht - UCLA
Contents: Basic Probability Theory (Conditional Probability, Random Variables, Limit Theorems); Elements of Statistics (Estimators, Tests, Distributions, Correlation and Covariance, Linear Regression, Markov Chains); Probabilistic Linguistics.
by Cosma Rohilla Shalizi
Contents: Probability (Probability Calculus, Random Variables, Discrete and Continuous Distributions); Statistics (Handling of Data, Sampling, Estimation, Hypothesis Testing); Stochastic Processes (Markov Processes, Continuous-Time Processes).
by D. A. Levin, Y. Peres, E. L. Wilmer - American Mathematical Society
An introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space.
by Christophe Garban, Jeffrey E. Steif - arXiv
The goal of this set of lectures is to combine two seemingly unrelated topics: (1) The study of Boolean functions, a field particularly active in computer science; (2) Some models in statistical physics, mostly percolation.