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A positive integer n is called a θ-congruent number if n sin θ is the area of a triangle with rational side lengths and with an angle θ. Markov chains play a key role in the study of the distribution ...
A number of biological systems can be modeled by Markov chains. Recently, there has been an increasing concern about when biological systems modeled by Markov chains will perform a dynamic phenomenon ...
A number of biological systems can be modeled by Markov chains. Recently, there has been an increasing concern about when biological systems modeled by Markov chains will perform a dynamic phenomenon ...
This paper develops bounds on the rate of decay of powers of Markov kernels on finite state spaces. These are combined with eigenvalue estimates to give good bounds on the rate of convergence to sta...
This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic So...
We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp resul...
A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular g...
We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools invo...
DE FINETTI'S THEOREM FOR MARKOV CHAINS.
We develop bounds for the second largest eigenvalue and spectral gap of a reversible Markov chain. The bounds depend on geometric quantities such as the maximum degree, diameter and covering numbe...
We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp r...
THREE EXAMPLES OF MONTE-CARLO MARKOV CHAINS:AT THE INTERFACE BETWEEN STATOSTICAL COMPUTING,COMPUTER SCIENCE,AND STATISTICAL MECHANICS
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
The cutoff phenomenon in finite Markov chains
We investigate how the stationary distribution of a Markov chain changes when transitions from a single state are modified. In particular, adding a single directed edge to nearest neighbor random wa...

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