Ranking graphs through hitting times of Markov chains

Abstract

In the present paper we show that for any given digraph 𝔾=([n],E→), that is, an oriented graph without self‐loops and 2‐cycles, one can construct a 1‐dependent Markov chain and n identically distributed hitting times T1, … , Tn on this chain such that the probability of the event Ti > Tj, for any i, j = 1, … , n, is larger than 12 if and only if (i,j)∈E→. This result is related to various paradoxes in probability theory, concerning in particular non‐transitive dice.

Construction of aggregation paradoxes through load-sharing models

“…In the recent paper [7] it has been proven for an arbitrary digraph G = ([m], E) that one can build a Markov chain and suitable associated hitting times X 1 , . .…”