Parking on a Random Tree

Abstract

Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Renyi's parking problem, alternatively called blocking RSA: at every vertex of the tree a particle (or car) arrives with rate one. The particle sticks to the vertex whenever the vertex and all of its nearest neighbors are not occupied yet. We provide an explicit expression for the so-called parking constant in terms of the generating function.

7 pages

References in corpus (2)

• Evolution of networks
• Exact and approximate results for deposition and annihilation processes on graphs

Cited by in corpus (8)

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• Dependent particle deposition on a graph: concentration properties of the height profile
• Multiple-Layer Parking with Screening
• Analytical Results for a Small Multiple-layer Parking System