Related papers: Markov branching in the vertex splitting model
We establish a new connection between metric Diophantine approximation and the parametric geometry of numbers by proving a variational principle facilitating the computation of the Hausdorff and packing dimensions of many sets of interest…
For $0<\alpha<1,$ and $\theta>-\alpha,$ let $(S^{-\alpha}_{\alpha,\theta+r})_{\{r\ge 0\}}$ denote an increasing(decreasing) sequence of variables forming a time inhomogeneous Markov chain whose marginal distributions are equivalent to…
We study the almost sure convergence of the occupation measure of evolution models where mutation rates decrease over time. We show that if the mutation parameter vanishes at a controlled rate, then the empirical occupation measure…
Consider the d-dimensional lattice Z^d where each vertex is ``open'' or ``closed'' with probability p or 1-p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth co-ordinates of v and w…
We discuss the scaling properties of free branched polymers. The scaling behaviour of the model is classified by the Hausdorff dimensions for the internal geometry: d_L and d_H, and for the external one: D_L and D_H. The dimensions d_H and…
We study a general model of recursive trees where vertices are equipped with independent weights and at each time-step a vertex is sampled with probability proportional to its fitness function (a function of its weight and degree) and…
Given a finite typed rooted tree $T$ with $n$ vertices, the {\em empirical subtree measure} is the uniform measure on the $n$ typed subtrees of $T$ formed by taking all descendants of a single vertex. We prove a large deviation principle in…
We study graphs whose vertex degree tends and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth.…
We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in (1,2)$. The limiting components are…
Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate scaling limits of finite dimensional population size Markov…
A Markov Additive Process is a bi-variate Markov process $(\xi,J)=\big((\xi_t,J_t),t\geq0\big)$ which should be thought of as a multi-type L\'evy process: the second component $J$ is a Markov chain on a finite space $\{1,\ldots,K\}$, and…
In typical single-molecule force spectroscopy experiments the mechanical unfolding of molecular complexes or biomolecules is studied applying a force ramp to one end of the system while the other end is kept fixed in space. The…
In this paper, we show the convergence rates of posterior distributions of the model dynamics in a MDP for both episodic and continuous tasks. The theoretical results hold for general state and action space and the parameter space of the…
Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…