arXiv subjects

R. J. Gava

Publications and source records attributed to R. J. Gava.

3 recordsLinked to original sources

arXiv2018

On the existence of accessibility in a tree-indexed percolation model

We study the accessibility percolation model on infinite trees. The model is defined by associating an absolute continuous random variable $X_v$ 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 $v_1,v_2,v_3\ldots$ such that $X_{v_1} 0$ is a given constant. We show that there is a percolation threshold at $α_c =1$ such that there is percolation if $α> 1$ and there is absence of percolation if $α\leq 1$. 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 $F^α$ record model. We also discuss a number of open problems concerning the accessibility percolation model for further consideration in future research.

math.PR↗

arXiv2014

The K-process on a tree as a scaling limit of the GREM-like trap model

We introduce trap models on a finite volume $k$-level tree as a class of Markov jump processes with state space the leaves of that tree. They serve to describe the GREM-like trap model of Sasaki and Nemoto. Under suitable conditions on the parameters of the trap model, we establish its infinite volume limit, given by what we call a $K$-process in an infinite $k$-level tree. From this we deduce that the $K$-process also is the scaling limit of the GREM-like trap model on extreme time scales under a fine tuning assumption on the volumes.

math.PR↗

arXiv2012

Scaling limits and aging for asymmetric trap models on the complete graph and K-processes

We obtain scaling limit results for asymmetric trap models and their infinite volume counterparts, namely asymmetric K processes. Aging results for the latter processes are derived therefrom.

math.PR↗