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pro vyhledávání: '"05C81, 60J10"'
In this paper, we determine a formula for Kemeny's constant for a graph with multiple bridges, in terms of quantities that are inherent to the subgraphs obtained upon removal of all bridges and that can be computed independently. With the formula, we
Externí odkaz:
http://arxiv.org/abs/2205.08235
Autor:
Wei, Zhi-Feng
Publikováno v:
Journal of Functional Analysis 284 (2023) 109799
Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In addition, spe
Externí odkaz:
http://arxiv.org/abs/2111.08777
Autor:
Olesker-Taylor, Sam, Zanetti, Luca
Publikováno v:
Probab. Theory Relat. Fields 188, 1017-1062 (2024)
In the Fastest Mixing Markov Chain problem, we are given a graph $G = (V, E)$ and desire the discrete-time Markov chain with smallest mixing time $\tau$ subject to having equilibrium distribution uniform on $V$ and non-zero transition probabilities o
Externí odkaz:
http://arxiv.org/abs/2111.05816
Publikováno v:
Combinatorics, Probability and Computing, 32(4):594 - 637, 2023
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover time of mult
Externí odkaz:
http://arxiv.org/abs/2011.07893
Autor:
Ozawa, Narutaka
It is recently proved by Lubetzky and Peres that the simple random walk on a Ramanujan graph exhibits a cutoff phenomenon, that is to say, the total variation distance of the random walk distribution from the uniform distribution drops abruptly from
Externí odkaz:
http://arxiv.org/abs/2009.00837
Publikováno v:
ACM Trans. Algorithms, 18(2), 2022
We study the biased random walk where at each step of a random walk a "controller" can, with a certain small probability, move the walk to an arbitrary neighbour. This model was introduced by Azar et al. [STOC'1992]; we extend their work to the time
Externí odkaz:
http://arxiv.org/abs/2006.02475
Publikováno v:
Phys. Rev. Lett. 127, 078301 (2021)
We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps
Externí odkaz:
http://arxiv.org/abs/2005.00337
Publikováno v:
Combinator. Probab. Comp. 31 (2022) 73-100
We apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this allows the con
Externí odkaz:
http://arxiv.org/abs/1911.05170
Autor:
Conchon--Kerjan, Guillaume
We prove a cutoff for the random walk on random $n$-lifts of finite weighted graphs, even when the random walk on the base graph $\mathcal{G}$ of the lift is not reversible. The mixing time is w.h.p. $t_{mix}=h^{-1}\log n$, where $h$ is a constant as
Externí odkaz:
http://arxiv.org/abs/1908.02898
Autor:
Caputo, Pietro, Quattropani, Matteo
We consider the generalised PageRank walk on a digraph $G$, with refresh probability $\alpha$ and resampling distribution $\lambda$. We analyse convergence to stationarity when $G$ is a large sparse random digraph with given degree sequences, in the
Externí odkaz:
http://arxiv.org/abs/1905.04993