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10 papers · 1 filter
Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing
Julien Allasia
In this paper, we study random walks evolving with a directional bias in a two-dimensional random environment with correlations that vanish polynomially. Using renormalization meth…
Self-interacting diffusions: long-time behaviour and exit-problem in the convex case
Ashot Aleksian, Pierre del Moral, Aline Kurtzmann +1
We study a class of time-inhomogeneous diffusion: the self-interacting one. We show a convergence result with a rate of convergence that does not depend on the diffusion coefficien…
On the exit-problem for self-interacting diffusions
Ashot Aleksian, Pierre Del Moral, Aline Kurtzmann +1
We study the exit-time from a domain of a self-interacting diffusion, where the Brownian motion is replaced by for a constant . The first part of this work consists in sh…
Asymptotic expansion of Toeplitz determinants of an indicator function with discrete rotational symmetry and powers of random unitary matrices
Olivier Marchal
In this short article we propose a full large asymptotic expansion of the probability that the power of a random unitary matrix of size has all its eigenval…
Fine asymptotics for the maximum degree in weighted recursive trees with bounded random weights
Laura Eslava, Bas Lodewijks, Marcel Ortgiese
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its…
On the modularity of 3-regular random graphs and random graphs with given degree sequences
Lyuben Lichev, Dieter Mitsche
The modularity of a graph is a parameter that measures its community structure; the higher its value (between and ), the more clustered the graph is. In this paper we show t…