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76 papers · 1 filter
Asymptotic properties of expansive Galton-Watson trees
Romain Abraham, Jean-François Delmas
We consider a super-critical Galton-Watson tree whose non-degenerate offspring distribution has finite mean. We consider the random trees n distributed as conditioned on the…
Probabilistic and Piecewise Deterministic models in Biology
Bertrand Cloez, Renaud Dessalles, Alexandre Genadot +3
We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by Davis (19…
Model Spaces of Regularity Structures for Space-Fractional SPDEs
Nils Berglund, Christian Kuehn
We study model spaces, in the sense of Hairer, for stochastic partial differential equations involving the fractional Laplacian. We prove that the fractional Laplacian is a singula…
An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two
Nils Berglund, Giacomo Di Gesù, Hendrik Weber
We study spectral Galerkin approximations of an Allen--Cahn equation over the two-dimensional torus perturbed by weak space-time white noise of strength . We in…
Critical Multi-Type Galton-Watson Trees Conditioned to be Large
Romain Abraham, Jean-François Delmas, Hongsong Guo
Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten…
Range and critical generations of a random walk on Galton-Watson trees
Pierre Andreoletti, Xinxin Chen
In this paper we consider a random walk in random environment on a tree and focus on the boundary case for the underlying branching potential. We study the range of this wal…