scholarly journals Cover times for sequences of reversible Markov chains on random graphs

2014 ◽  
Vol 54 (3) ◽  
pp. 555-576 ◽  
Author(s):  
Yoshihiro Abe
Keyword(s):  
Markov Chains ◽  
Random Graphs ◽  
Cover Times ◽  
Reversible Markov Chains

scholarly journals A Spectral Characterization for Concentration of the Cover Time

2019 ◽  
Vol 33 (4) ◽  
pp. 2167-2184
Author(s):  
Jonathan Hermon
Keyword(s):  
Markov Chains ◽  
Spectral Gap ◽  
Hitting Time ◽  
Spectral Characterization ◽  
Cover Time ◽  
Cover Times ◽  
Reversible Markov Chains ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

Abstract We prove that for a sequence of finite vertex-transitive graphs of increasing sizes, the cover times are asymptotically concentrated if and only if the product of the spectral gap and the expected cover time diverges. In fact, we prove this for general reversible Markov chains under the much weaker assumption (than transitivity) that the maximal hitting time of a state is of the same order as the average hitting time.

Geometric L 2 and L 1 convergence are equivalent for reversible Markov chains

2001 ◽  
Vol 38 (A) ◽  
pp. 37-41 ◽  
Author(s):  
Gareth O. Roberts ◽  
Richard L. Tweedie
Keyword(s):  
Markov Chains ◽  
Queueing Models ◽  
Gibbs Samplers ◽  
Reversible Markov Chains

The paper proves the statement of the title, and shows that it has useful applications in evaluating the convergence of queueing models and Gibbs samplers with deterministic and random scans.

On the invariance principle for reversible Markov chains

2016 ◽  
Vol 53 (2) ◽  
pp. 593-599 ◽  
Author(s):  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Stochastic Processes ◽  
Partial Sums ◽  
Additive Functionals ◽  
Functional Clt ◽  
Reversible Markov Chains ◽  
Functional Central Limit

Abstract In this paper we investigate the functional central limit theorem (CLT) for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation of partial sums. For this case, we show that the functional CLT is equivalent to the fact that the variance of partial sums is regularly varying with exponent 1 and the partial sums satisfy the CLT. It is also equivalent to the conditional CLT.

On the Convergence of Reversible Markov Chains

1993 ◽  
Vol 14 (4) ◽  
pp. 950-966 ◽  
Author(s):  
Madhav P. Desai ◽  
Vasant B. Rao
Keyword(s):  
Markov Chains ◽  
Reversible Markov Chains

Geometric L2 and L1 convergence are equivalent for reversible Markov chains

2001 ◽  
Vol 38 (A) ◽  
pp. 37-41 ◽  
Author(s):  
Gareth O. Roberts ◽  
Richard L. Tweedie
Keyword(s):  
Markov Chains ◽  
Queueing Models ◽  
Gibbs Samplers ◽  
Reversible Markov Chains

The paper proves the statement of the title, and shows that it has useful applications in evaluating the convergence of queueing models and Gibbs samplers with deterministic and random scans.

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