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Theorem 1.2. Proof of Theorem 1.1. We will use the following auxiliary results in the proof.. Let SvwT denote the graph obtained from disjoint graphs S, T by adding an edge joining
Let ψ and W be as described in the second part of the statement of the theorem and let φ denote the Laplace exponent of the descending ladder height subordinator associated to
Keywords stable regenerative set, Bochner’s subordination, Bolthausen-Sznitman coalescent, Poisson covering, zero sets of Bessel processes, two parameter Poisson-Dirichlet
In the following we give a short description of the standard branching random walk, its intrinsic martingales and an associated multiplicative random walk.. Consider a
Recently, in [MR07c], we have shown that the edge-reinforced random walk on any locally finite graph has the same distribution as a random walk in a random environment given by
We emphasise that the scaling limit of the kinetic prudent walk seems to be different from the scaling limit of the uniform prudent walk studied in Combinatorics... The inset is
This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined
