scholarly journals Recurrence and transience of a multi-excited random walk on a regular tree

2009 ◽  
Vol 14 (0) ◽  
pp. 1628-1669 ◽  
Author(s):  
Anne-Laure Basdevant ◽  
Arvind Singh
Keyword(s):  
Random Walk ◽  
Regular Tree ◽  
Excited Random Walk

scholarly journals Upper and lower bounds on the speed of a one-dimensional excited random walk

2019 ◽  
Vol 12 (1) ◽  
pp. 97-115
Author(s):  
Erin Madden ◽  
Brian Kidd ◽  
Owen Levin ◽  
Jonathon Peterson ◽  
Jacob Smith ◽  
...  
Keyword(s):  
Random Walk ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
Excited Random Walk

scholarly journals On a general many-dimensional excited random walk

2012 ◽  
Vol 40 (5) ◽  
pp. 2106-2130 ◽  
Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Alejandro F. Ramírez ◽  
Marina Vachkovskaia
Keyword(s):  
Random Walk ◽  
Excited Random Walk

scholarly journals Excited Random Walk

2003 ◽  
Vol 8 (0) ◽  
pp. 86-92 ◽  
Author(s):  
Itai Benjamini ◽  
David Wilson
Keyword(s):  
Random Walk ◽  
Excited Random Walk

scholarly journals A balanced excited random walk

2011 ◽  
Vol 349 (7-8) ◽  
pp. 459-462 ◽  
Author(s):  
Itaı Benjamini ◽  
Gady Kozma ◽  
Bruno Schapira
Keyword(s):  
Random Walk ◽  
Excited Random Walk

scholarly journals The excited random walk in one dimension

2005 ◽  
Vol 38 (12) ◽  
pp. 2555-2577 ◽  
Author(s):  
T Antal ◽  
S Redner
Keyword(s):  
Random Walk ◽  
One Dimension ◽  
Excited Random Walk

scholarly journals Coverings, Laplacians, and Heat Kernels of Directed Graphs

10.37236/120 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Clara E. Brasseur ◽  
Ryan E. Grady ◽  
Stratos Prassidis
Keyword(s):  
Random Walk ◽  
Heat Kernel ◽  
Directed Graphs ◽  
Heat Kernels ◽  
Total Space ◽  
Regular Tree ◽  
Combinatorial Laplacian

Combinatorial covers of graphs were defined by Chung and Yau. Their main feature is that the spectra of the Combinatorial Laplacian of the base and the total space are related. We extend their definition to directed graphs. As an application, we compute the spectrum of the Combinatorial Laplacian of the homesick random walk $RW_{\mu}$ on the line. Using this calculation, we show that the heat kernel on the weighted line can be computed from the heat kernel of '$(1 + 1/\mu)$-regular' tree.

scholarly journals Excited random walk with periodic cookies

2016 ◽  
Vol 52 (3) ◽  
pp. 1023-1049
Author(s):  
Gady Kozma ◽  
Tal Orenshtein ◽  
Igor Shinkar
Keyword(s):  
Random Walk ◽  
Excited Random Walk

scholarly journals Excited random walk against a wall

2007 ◽  
Vol 140 (1-2) ◽  
pp. 83-102 ◽  
Author(s):  
Gideon Amir ◽  
Itai Benjamini ◽  
Gady Kozma
Keyword(s):  
Random Walk ◽  
Excited Random Walk

scholarly journals CUTOFF AT THE ENTROPIC TIME FOR RANDOM WALKS ON COVERED EXPANDER GRAPHS

2021 ◽  
pp. 1-46
Author(s):  
Charles Bordenave ◽  
Hubert Lacoin
Keyword(s):  
Random Walk ◽  
Lower Bound ◽  
Random Walks ◽  
Mixing Time ◽  
Simple Random Walk ◽  
Sufficient Condition ◽  
Regular Graphs ◽  
Expander Graphs ◽  
Transitive Graph ◽  
Regular Tree

Abstract It is a fact simple to establish that the mixing time of the simple random walk on a d-regular graph $G_n$ with n vertices is asymptotically bounded from below by $\frac {d }{d-2 } \frac {\log n}{\log (d-1)}$ . Such a bound is obtained by comparing the walk on $G_n$ to the walk on d-regular tree $\mathcal{T} _d$ . If one can map another transitive graph $\mathcal{G} $ onto $G_n$ , then we can improve the strategy by using a comparison with the random walk on $\mathcal{G} $ (instead of that of $\mathcal{T} _d$ ), and we obtain a lower bound of the form $\frac {1}{\mathfrak{h} }\log n$ , where $\mathfrak{h} $ is the entropy rate associated with $\mathcal{G} $ . We call this the entropic lower bound. It was recently proved that in the case $\mathcal{G} =\mathcal{T} _d$ , this entropic lower bound (in that case $\frac {d }{d-2 } \frac {\log n}{\log (d-1)}$ ) is sharp when graphs have minimal spectral radius and thus that in that case the random walk exhibits cutoff at the entropic time. In this article, we provide a generalisation of the result by providing a sufficient condition on the spectra of the random walks on $G_n$ under which the random walk exhibits cutoff at the entropic time. It applies notably to anisotropic random walks on random d-regular graphs and to random walks on random n-lifts of a base graph (including nonreversible walks).

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