Related papers: Coupling on weighted branching trees
We investigate a class of line ensembles whose local structure is described by independent geometric random walk bridges, which have been conditioned to interlace with each other. The latter arise naturally in the context Schur processes,…
We study the local convergence of critical Galton-Watson trees and Levy trees under various conditionings. Assuming a very general monotonicity property on the functional of random trees, we show that random trees conditioned to have large…
This thesis examines linearly edge-reinforced random walks on infinite trees. In particular, recurrence and transience of such random walks on general (fixed) trees as well as on Galton-Watson trees (i.e. random trees) is characterized, and…
Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear…
We consider simply generated trees and study multiplicative functions on rooted plane trees. We show that the associated generating functions satisfy differential equations or difference equations. Our approach considers B-series from…
These notes were used in a short graduate course on branching processes the author gave in Beijing Normal University. The following main topics are covered: scaling limits of Galton--Watson processes, continuous-state branching processes,…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Let $X_n(k)$ be the number of vertices at level $k$ in a random recursive tree with $n+1$ vertices. We prove a functional limit theorem for the vector-valued process $(X_{[n^t]}(1),\ldots, X_{[n^t]}(k))_{t\geq 0}$, for each $k\in\mathbb N$.…
A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic…
We consider weighted generating functions of trees where the weights are products of functions of the sizes of the subtrees. This work begins with the observation that three different communities, largely independently, found substantially…
Under the assumption that sequences of graphs equipped with resistances, associated measures, walks and local times converge in a suitable Gromov-Hausdorff topology, we establish asymptotic bounds on the distribution of the…
Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances…
This paper is concerned with convergence estimates for fully discrete tree tensor network approximations of high-dimensional functions from several model classes. For functions having standard or mixed Sobolev regularity, new estimates…
The rotor-router model is a deterministic process analogous to a simple random walk on a graph. This paper is concerned with a generalized model, functional-router model, which imitates a Markov chain possibly containing irrational…
A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and…
This article develops general conditions for weak convergence of adaptive Markov chain Monte Carlo processes and is shown to imply a weak law of large numbers for bounded Lipschitz continuous functions. This allows an estimation theory for…
We consider connectivity properties of the Branching Interlacements model in $\mathbb{Z}^d,~d\ge5$, recently introduced by Angel, R\'ath and Zhu in 2016. Using stochastic dimension techniques we show that every two vertices visited by the…
Under natural conditions, we proved the exponential ergodicity in Wasserstein distance of two-type continuous-state branching processes in L\'evy random environments with immigration. Furthermore, we expressed accurately the parameters of…
A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and…