165 citations · 259 across the 55 of their papers we have counts for
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Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion
Elena Perfilev, Vitali Wachtel
This note is devoted to the study of the maximum of the excursion of a random walk with negative drift and light-tailed increments. More precisely, we determine the local asymptoti…
Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments
Denis Denisov, Elena Perfilev, Vitali Wachtel
We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asympto…
Renewal Theory for Transient Markov Chains with Asymptotically Zero Drift
Denis Denisov, Dmitry Korshunov, Vitali Wachtel
We solve the problem of asymptotic behaviour of the renewal measure (Green function) generated by a transient Lamperti's Markov chain in , that is, when the drift…
Tightness and Line Ensembles for Brownian Polymers under Geometric Area Tilts
Pietro Caputo, Dmitry Ioffe, Vitali Wachtel
We prove tightness and limiting Brownian-Gibbs description for line ensembles of non-colliding Brownian bridges above a hard wall, which are subject to geometrically growing self-p…