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

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	783-785
Number of pages	3
Journal	Statistics and Probability Letters
Volume	82
Issue number	4
DOIs	https://doi.org/10.1016/j.spl.2011.12.012
State	Published - Apr 2012
Externally published	Yes

Keywords

Effective resistance
Kirchhoff index

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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 - Palacios, José Luis

AU - Renom, José M.

PY - 2012/4

Y1 - 2012/4

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84856297064&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2011.12.012

DO - 10.1016/j.spl.2011.12.012

M3 - Article

AN - SCOPUS:84856297064

SN - 0167-7152

VL - 82

SP - 783

EP - 785

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

On partial sums of hitting times

Abstract

Keywords

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