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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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Reversals and Transpositions Over Finite Alphabets
Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition, orExpand
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Graphs induced by Gray codes
We disprove a conjecture of Bultena and Ruskey (Electron. J. Combin. 3 (1996) R11), that all trees which are cyclic graphs of cyclic Gray codes have diameter 2 or 4, by producing codes whose cyclicExpand
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COMPARING EIGENVALUE BOUNDS FOR MARKOV CHAINS: WHEN DOES POINCARE BEAT CHEEGER?
The Poincaré and Cheeger bounds are two useful bounds for the second largest eigenvalue of a reversible Markov chain. Diaconis and Stroock [1991] and Jerrum and Sinclair [1989] develop versions ofExpand
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Combinatorics in the exterior algebra and the Bollob\'{a}s Two Families Theorem.
We investigate the combinatorial structure of subspaces of the exterior algebra of a finite-dimensional real vector space, working in parallel with the extremal combinatorics of hypergraphs. As anExpand
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Coupling from the past
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Hypergraphs of Bounded Disjointness
TLDR
A $k$-uniform hypergraph is $s$-almost intersecting if every edge is disjoint from exactly$s$ other edges. Expand
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A Local Limit Theorem for a Family of Non-Reversible Markov Chains
By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging identicalExpand
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