相关论文: Global Regime for General Additive Functionals of …

Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. This paper is devoted to…

We consider the Ising model on a supercritical Galton-Watson tree $\mathbf{T}_n$ of depth $n$ with a sparse random external field, given by a collection of i.i.d. Bernouilli random variables with vanishing parameter $p_n$. This may me…

We establish a general sufficient condition for a sequence of Galton Watson branching processes in varying environment to converge weakly. This condition extends previous results by allowing offspring distributions to have infinite…

We study $\lambda$-biased branching random walks on Bienaym\'e--Galton--Watson trees in discrete time. We consider the maximal displacement at time $n$, $\max_{\vert u \vert =n} \vert X(u) \vert$, and show that it almost surely grows at a…

We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the…

We design exact polynomial expansions of a class of Feynman--Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any…

This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…

Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…

Various combinatorial classes such as outerplanar graphs and maps, series-parallel graphs, substitution-closed classes of permutations and many more allow bijective encodings by so-called enriched trees, which are rooted trees with…

We provide a simple forest model to encode the genealogical structure of a multitype Galton-Watson process with immigration. We provide two encodings of these forests by stochastic processes. We show, under appropriate conditions, the…

In this paper we consider random walks on Galton-Watson trees with random conductances. On these trees, the distance of the walker to the root satisfies a law of large numbers with limit the effective velocity, or speed of the walk. We…

We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius $n$ centered at the root, we prove that, although the size of the boundary is of order $n$, most of the harmonic measure is supported…

In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of…

We consider an interacting particle system on trees known as the frog model: initially, a single active particle begins at the root and i.i.d.~$\mathrm{Poiss}(\lambda)$ many inactive particles are placed at each non-root vertex. Active…

Most systems, when pushed out of equilibrium, respond by building up currents of locally-conserved observables. Understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open…

We consider branching random walks built on Galton-Watson trees with offspring distribution having a bounded support, conditioned to have $n$ nodes, and their rescaled convergences to the Brownian snake. We exhibit a notion of "globally…

In the regime of Galton-Watson trees, first order logic statements are roughly equivalent to examining the presence of specific finite subtrees. We consider the space of all trees with Poisson offspring distribution and show that such…

In this article, we prove a joint large deviation principle in $n$ for the \emph{empirical pair measure} and \emph{ empirical offspring measure} of critical multitype Galton-Watson trees conditioned to have exactly $n$ vertices in the weak…

We give a simplified and more complete description of the loop variable approach for writing down gauge invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of…

Consider a supercritical Bienaym\'e--Galton--Watson tree $ \mathcal{T}$ with geometric offspring distribution. Each vertex of this tree represents a parking spot which can accommodate at most one car. On the top of this tree, we add $(A_u :…