منابع مشابه
The cutoff phenomenon in finite Markov chains.
Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to ...
متن کاملThe cutoff phenomenon for random birth and death chains
For any distribution π on {1, 2, . . . , n}, we study elements drawn at random from the set Aπ of tridiagonal stochastic matrices K satisfying π(i)K[i, j] = π(j)K[j, i] for all i, j ∈ [n]. These matrices correspond to birth and death chains with stationary distribution π. We analyze an algorithm for sampling from Aπ and use results from this analysis to draw conclusions about typical elements o...
متن کاملThe cutoff phenomenon for randomized riffle shuffles
We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.
متن کاملThe cutoff phenomenon for ergodic Markov processes
We consider the cutoff phenomenon in the context of families of ergodic Markov transition functions. This includes classical examples such as families of ergodic finite Markov chains and Brownian motion on families of compact Riemannian manifolds. We give criteria for the existence of a cutoff when convergence is measured in L-norm, 1 < p < ∞. This allows us to prove the existence of a cutoff i...
متن کاملA Numerical Analyst Looks at the "Cutoff Phenomenon" in Card Shuffling and Other Markov Chains
Acknowledgement This paper was prompted in part by an inspiring course taught at Cornell by Persi Diaconis in the fall of 1996. For help and advice along the way we are grateful to Diaconis and to 29 References 1] D. Bayer and P. Diaconis, \Trailing the dovetail shuue to its lair," Ann. Appl. \Asymptotic analysis of a random walk on a hypercube with many dimensions," Random Struct. and Alg.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2012
ISSN: 0304-4149
DOI: 10.1016/j.spa.2012.05.003