相关论文: Random Combinatorial structures:the convergent cas…

We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…

Given a sequence of integers $a_j, j\ge 1,$ a multiset is a combinatorial object composed of unordered components, such that there are exactly $a_j$ one-component multisets of size $j.$ When $a_j\asymp j^{r-1} y^j$ for some $r>0$, $y\geq…

We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the…

We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…

We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…

Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and $p$-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar…

The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…

The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a…

In contrast to the canonically conjugate variates $q$,$p$ representing the position and momentum of a particle in the phase space distributions, the three Cartesian components, $J_{x}$,$J_{y}$, $J_{z}$ of a spin-$j$ system constitute the…

For fixed $t\ge 2$, we consider the class of representations of $1$ as sum of unit fractions whose denominators are powers of $t$ or equivalently the class of canonical compact $t$-ary Huffman codes or equivalently rooted $t$-ary plane…

It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent $\gamma>3$, the largest component is of order $n^{1/(\gamma-1)}$. More precisely, the order of the largest…

Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…

In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than one, the random linear recurrence goes exponentially fast to…

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e.,…

We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…

This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…