The scaling limit of the interface of the continuous-space symbiotic branching model JOCHEN BLATH, MATTHIAS HAMMER AND MARCEL ORTGIESE 807 A noncommutative martingale convexity inequality . . . . . .â€¦ (More)

We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on theâ€¦ (More)

Abstract: In the first part of this paper we give easy and intuitive proofs for the small value probabilities of the martingale limit of a supercritical Galton-Watson process in both the SchrÃ¶der andâ€¦ (More)

We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this modelâ€¦ (More)

The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportionalâ€¦ (More)

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show that the system of particles, rescaled in an appropriate way,â€¦ (More)

The symbiotic branching model describes a spatial population consisting of two types that are allowed to migrate in space and branch locally only if both types are present. We continue ourâ€¦ (More)

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of theâ€¦ (More)

The symbiotic branching model describes the evolution of two interacting populations and if started with complementary Heaviside functions, the interface where both populations are present remainsâ€¦ (More)

The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlyingâ€¦ (More)