Travelling wave solutions to the K-P-P equation at supercritical wave speeds: a parallel to Simon Harris' probabilistic analysis

Abstract

Recently Harris using probabilistic methods alone has given new proofs for the known existence asymptotics and unique ness of travelling wave solutions to the KPP equation Following in this vein we outline alternative probabilistic proofs for wave speeds exceeding the critical minimal wave speed Speci cally the analysis is con ned to the study of additive and multiplicative martingales and the construction of size biased measures on the space of marked trees generated by the branching process This paper also acts as a prelude to its companion Kyprianou b which deals with the more dif cult case of travelling waves at criticality The importance of these new probabilistic proofs is their generic nature which in principle can be extended to study other types of spatial branching di usions and associated travelling waves