2014/10/31 by Cristian F. Coletti, Renato Jacob Gava, R. J. Gava +2 · 7 citations
Computer Science · Mathematics · Physics and Astronomy · Psychology · #Combinatorics #Complex Network Analysis Techniques #Continuum percolation theory #Critical exponent #Data Management and Algorithms #Directed percolation #Geometry #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Physics #Psychology #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #Tree (set theory) #math.PR
paper · pdf · open access · doi:10.1016/j.physa.2017.10.019
published in Physica A Statistical Mechanics and its Applications 492, 382-388 (Elsevier BV) · This version has been partially rewritten due to a mistake in the proof of the main theorem in the previous version. New arguments have been used to prove the main result for a different family of growth functions. Other properties of the model, such as the existence of accessibility percolation infinitely often on the supercritical regime, have been studied
openalex publication_date 2017/10/31 · arxiv created 2018/03/22 · arxiv updated 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the accessibility percolation model on infinite trees. The model is defined by associating an absolute continuous random variable Xv to each vertex v of the tree. The main question to be considered is the existence or not of an infinite path of nearest neighbors v1,v2,v3… such that Xv1<Xv2<Xv3<⋯ and which spans the entire graph. The event defined by the existence of such path is called \itpercolation. We consider the case of the accessibility percolation model on a spherically symmetric tree with growth function given by f(i)=\lceil (i+1)^ α \rceil, where α>0 is a given constant. We show that there is a percolation threshold at αc =1 such that there is percolation if α> 1 and there is absence of percolation if α ≤ 1. Moreover, we study the event of percolation starting at any vertex, as well as the continuity of the percolation probability function. Finally, we provide a comparison between this model with the well known Fα record model. We also discuss a number of open problems concerning the accessibility percolation model for further consideration in future research.