Related papers: Frog models on trees through renewal theory

We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…

We propose a tree regularization framework, which enables many tree models to perform feature selection efficiently. The key idea of the regularization framework is to penalize selecting a new feature for splitting when its gain (e.g.…

This paper investigates functional limit theorems for the Elephant Random Walk (ERW) on general periodic structures, extending the Bertenghi's results on $\mathbb{Z}^d$. Our results reveal new structure-dependent quantities that do not…

This paper investigates the large deviation problem in the sample path space of the nearest-neighbor random walks on regular trees. We establish the sample path large deviation principle for the law of the distance from a nearest random…

We take scaling limits of the Bouchaud and Dean trap model on Parisi's tree in time scales where the dynamics is either ergodic (close to equilibrium) or aging (far from equilibrium). These results follow from a continuity theorem…

We consider loop ensembles on random trees. The loops are induced by a Poisson process of links sampled on the underlying tree interpreted as a metric graph. We allow two types of links, crosses and double bars. The crosses-only case…

We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter $\alpha$ which governs the strength of the reinforcement, and a collection of Poisson processes indexed by the vertices of the…

It is a celebrated fact that a simple random walk on an infinite $k$-ary tree for $k \geq 2$ returns to the initial vertex at most finitely many times during infinitely many transitions; it is called transient. This work points out the fact…

In this paper, we investigate random walks in a family of small-world trees having an exponential degree distribution. First, we address a trapping problem, that is, a particular case of random walks with an immobile trap located at the…

Network growth models that embody principles such as preferential attachment and local attachment rules have received much attention over the last decade. Among various approaches, random walks have been leveraged to capture such…

Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…

Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…

The rate at which nodes in evolving social networks acquire links (friends, citations) shows complex temporal dynamics. Preferential attachment and link copying models, while enabling elegant analysis, only capture rich-gets-richer effects,…

We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter $\beta>0$ per edge. This is called the arboreal gas model, and the special case when $\beta=1$ is the uniform forest…

Survival and percolation probabilities are most important quantities in the theory and in the application of growth models with spreading. We construct field theoretical expressions for these probabilities which are feasible for…

Galled trees are studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into tree-child, galled and reticulation-visible network classes by relaxing a structural condition imposed on…

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…

The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…

We consider a long-range percolation model on homogeneous oriented trees with several lengths. We obtain the critical surface as the set of zeros of a specific polynomial with coefficients depending explicitly on the lengths and the degree…

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…