Fixed speed competition on the configuration model with infinite variance degrees: unequal speeds

TL;DR

This paper analyzes how two competing spreading processes with fixed speeds behave on a random graph with infinite variance degrees, showing that the faster process dominates almost entirely when speeds differ.

Contribution

It introduces a model of competing spreads with fixed speeds on the configuration model with heavy-tailed degrees, revealing dominance of the faster spread.

Findings

Faster color paints almost all vertices when speeds differ.

Slower color is limited to a subpolynomial fraction of vertices.

Equal speeds case is deferred to future work.

Abstract

We study competition of two spreading colors starting from single sources on the configuration model with i.i.d. degrees following a power-law distribution with exponent tau in (2,3). In this model two colors spread with a fixed but not necessarily equal speed on the unweighted random graph. We show that if the speeds are not equal, then the faster color paints almost all vertices, while the slower color can paint only a random subpolynomial fraction of the vertices. We investigate the case when the speeds are equal and typical distances in a follow-up paper.