540 citations
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5 papers · 1 filter
The conditioned reconstructed process
Tanja Gernhard
We investigate a neutral model for speciation and extinction, the constant rate birth-death process. The process is conditioned to have extant species today, we look at the tre…
Local probabilities for random walks conditioned to stay positive
Vladimir Vatutin, Vitali Wachtel
Let S_0=0,{S_n, n>0} be a random walk generated by a sequence of i.i.d. random variables X_1,X_2,... and let τ^{-} be the first descending ladder epoch. Assuming that the distribut…
Polymer pinning in a random medium as influence percolation
Vincent Beffara, Vladas Sidoravicius, Herbert Spohn +1
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard meth…
A central limit theorem for Gibbs measures relative to Brownian motion
Volker Betz, Herbert Spohn
We study a Gibbs measure over Brownian motion with a pair potential which depends only on the increments. Assuming a particular form of this pair potential, we establish that in th…
Constrained Brownian motion: Fluctuations away from circular and parabolic barriers
Patrik L. Ferrari, Herbert Spohn
Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(\pm T)=0 conditioned to stay above the semicircle c_T(t)=\sqrtT^2-t^2. In the limit of large T,…