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Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…

Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…

We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

We consider line ensembles of non-intersecting random walks constrained by a hard wall, each tilted by the area underneath it with geometrically growing pre-factors $\mathfrak{b}^i$ where $\mathfrak{b}>1$. This is a model for the level…

We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and…

Aldous and Pitman (1994) studied asymptotic distributions, as n tends to infinity, of various functionals of a uniform random mapping of a set of n elements, by constructing a mapping-walk and showing these mapping-walks converge weakly to…

This paper analyzes a random walk model for the level lines appearing in the entropic repulsion phenomena of three-dimensional discrete random interfaces above a hard wall; we are particularly motivated by the low-temperature (2+1)D…

This study provides a foundational theoretical investigation into the mathematical existence and asymptotic properties of Ulanowicz's structural resilience. While ecological evidence suggests that sustainable systems gravitate toward an…

We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the…

We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…

We propose a new model and estimation framework for spatiotemporal streamflow exceedances above a threshold that flexibly captures asymptotic dependence and independence in the tail of the distribution. We model streamflow using a mixture…

We obtain a complete description of anisotropic scaling limits of random grain model on the plane with heavy tailed grain area distribution. The scaling limits have either independent or completely dependent increments along one or both…

We consider dense graph sequences that converge to a connected graphon and prove that the GHP scaling limit of their uniform spanning trees is Aldous' Brownian CRT. Furthermore, we are able to extract the precise scaling constant from the…

We prove that critical multitype Galton-Watson trees converge after rescaling to the Brownian continuum random tree, under the hypothesis that the offspring distribution has finite covariance matrices. Our study relies on an ancestral…

We encode a certain class of stochastic fragmentation processes, namely self-similar fragmentation processes with a negative index of self-similarity, into a metric family tree which belongs to the family of Continuum Random Trees of…

We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a $d$-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for frog…

Stochastic networks based on random point sets as nodes have attracted considerable interest in many applications, particularly in communication networks, including wireless sensor networks, peer-to-peer networks and so on. The study of…

It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in…

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…