On partial sums of hitting times

José Luis Palacios; José M. Renom

doi:10.1016/j.spl.2011.12.012

On partial sums of hitting times

José Luis Palacios, José M. Renom

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3 Citas (Scopus)

Resumen

We conjecture that if T _j is the hitting time of vertex j then ∑jEiTj≥(N-1)2, for all i, for a random walk on any connected graph G=(V, E) with {pipe}E{pipe}=N. We prove the conjecture for a family of graphs containing the regular graphs and obtain slightly better bounds for trees and non-regular edge-transitive graphs.

Idioma original	Inglés
Páginas (desde-hasta)	783-785
Número de páginas	3
Publicación	Statistics and Probability Letters
Volumen	82
N.º	4
DOI	https://doi.org/10.1016/j.spl.2011.12.012
Estado	Publicada - abr. 2012
Publicado de forma externa	Sí

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10.1016/j.spl.2011.12.012

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title = "On partial sums of hitting times",

abstract = "We conjecture that if T j is the hitting time of vertex j then ∑jEiTj≥(N-1)2, for all i, for a random walk on any connected graph G=(V, E) with {pipe}E{pipe}=N. We prove the conjecture for a family of graphs containing the regular graphs and obtain slightly better bounds for trees and non-regular edge-transitive graphs.",

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AU - Renom, José M.

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AB - We conjecture that if T j is the hitting time of vertex j then ∑jEiTj≥(N-1)2, for all i, for a random walk on any connected graph G=(V, E) with {pipe}E{pipe}=N. We prove the conjecture for a family of graphs containing the regular graphs and obtain slightly better bounds for trees and non-regular edge-transitive graphs.

KW - Effective resistance

KW - Kirchhoff index

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M3 - Article

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JO - Statistics and Probability Letters

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On partial sums of hitting times

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