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math.PR2018
The branching-ruin number as critical parameter of random processes on trees
Andrea Collevecchio, Cong Bang Huynh, Daniel Kious
The branching-ruin number of a tree, which describes its asymptotic growth and geometry, can be seen as a polynomial version of the branching number. This quantity was defined by C…
math.PR2018
Once reinforced random walk on
Daniel Kious, Bruno Schapira, Arvind Singh
We revisit an unpublished paper of Vervoort (2002) on the once reinforced random walk, and prove that this process is recurrent on any graph of the form , with…
math.PR2018
Explicit formula for the density of local times of Markov Jump Processes
Ruojun Huang, Daniel Kious, Vladas Sidoravicius +1
In this note we show a simple formula for the joint density of local times, last exit tree and cycling numbers of continuous-time Markov Chains on finite graphs, which involves the…