相关论文: Random environment on coloured trees

We define decorated $\alpha$-stable trees which are informally obtained from an $\alpha$-stable tree by blowing up its branchpoints into random metric spaces. This generalizes the $\alpha$-stable looptrees of Curien and Kortchemski, where…

In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…

Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…

In this article we consider several probabilistic processes defining random grapha. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each of the probabilistic processes, we…

Cayley's formula states that the number of labelled trees on $n$ vertices is $n^{n-2}$, and many of the current proofs involve complex structures or rigorous computation. We present a bijective proof of the formula by providing an…

We are interested in the independence number of large random simply generated trees and related parameters, such as their matching number or the kernel dimension of their adjacency matrix. We express these quantities using a canonical…

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…

Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the…

This paper outlines a method to determine whether two label-regular directed trees, are isomorphic and when they are almost isomorphic. The approach involves reinterpreting label-regular directed trees as universal covers of rooted graphs.…

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…

By developing the entropy theory of random walks on equivalence relations and analyzing the asymptotic geometry of horospheric products we describe the Poisson boundary for random walks on random horospheric products of trees.

We adapt the idea of random projections applied to the output space, so as to enhance tree-based ensemble methods in the context of multi-label classification. We show how learning time complexity can be reduced without affecting…

We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…

We study a broad class of random labelled trees in which integer-valued labels evolve along the edges according to increments in $\{-1, 0, 1\}$. These models include e.g. branching random walks, embedded complete and incomplete binary…

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…

Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…

We propose a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is sampled at time zero only; (II) the random environment is resampled at every…