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Markov Chains and Mixing Times
This book is 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 stationaryExpand
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Harnack Inequalities for Jump Processes
We consider a class of pure jump Markov processes in Rd whose jump kernels are comparable to those of symmetric stable processes. We establish a Harnack inequality for nonnegative functions that areExpand
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Transition Probabilities for Symmetric Jump Processes
We consider symmetric Markov chains on the integer lattice in d dimensions, where a ∈ (0, 2) and the conductance between x and y is comparable to |x-y| -(d+α) . We establish upper and lower boundsExpand
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Markov Chains and Mixing Times: Second Edition
TLDR
Unlike most books reviewed in the Intelligencer this is definitely a textbook. Expand
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Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability
We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie–Weiss Model. For β < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarityExpand
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A Phase Transition in Random coin Tossing
Suppose that a coin with bias θ is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let μ θ be the distribution of the observed sequence of coin tosses, andExpand
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Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path
TLDR
This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. Expand
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A Fourier-analytic approach to counting partial Hadamard matrices
TLDR
The existence of partial Hadamard matrices can be proved by showing that there is positive probability of a random walk returning to the origin after a specified number of steps. Expand
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Identifying several biased coins encountered by a hidden random walk
  • D. Levin, Y. Peres
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • 22 April 2003
TLDR
We can determine the biases {θ(z)}z∈Z, using only the outcomes of these coin tosses and no information about the path of the random walker, up to a shift and reflection of Z. Expand
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Continuous and discontinuous phase transitions in hypergraph processes
Let V denote a set of N vertices. To construct a hypergraph process, create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with generatingExpand
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