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In 1993 van den Berg and Kesten proved a strict monotonicity theorem for first passage percolation on $\mathbb{Z}^d$, $d \ge 2$: given two probability measures $\nu$ and $\tilde{\nu}$ with finite mean, if $\tilde{\nu}$ is strictly more…

Probability · Mathematics 2022-08-31 Christian Gorski

The hardcore model is a model of lattice gas systems which has received much attention in statistical physics, probability theory and theoretical computer science. It is the probability distribution over independent sets $I$ of a graph…

Computational Complexity · Computer Science 2010-06-01 Allan Sly

We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a…

Probability · Mathematics 2022-07-11 Matyas Barczy , Fanni K. Nedényi , Gyula Pap

Consider a point particle moving through a Poisson distributed array of cubes all oriented along the axes - the random wind-tree model introduced in Ehrenfest-Ehrenfest (1912). We show that, in the joint Boltzmann-Grad and diffusive limit…

Probability · Mathematics 2019-12-06 Christopher Lutsko , Bálint Tóth

In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…

Analysis of PDEs · Mathematics 2019-09-04 Fabian Christowiak , Carolin Kreisbeck

This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…

Machine Learning · Statistics 2020-06-18 Yuancheng Xu , Athanasse Zafirov , R. Michael Alvarez , Dan Kojis , Min Tan , Christina M. Ramirez

We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-01 Shay Kutten , Peter Robinson , Ming Ming Tan

Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…

Optimization and Control · Mathematics 2024-06-05 Ashwani Aggarwal

Motivated by the work of Lov\'asz and Szegedy on the convergence and limits of dense graph sequences, we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. Based on separable real trees,…

Combinatorics · Mathematics 2021-10-19 Gábor Elek , Gábor Tardos

We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from…

Probability · Mathematics 2008-07-04 Bo Chen , Daniel Ford , Matthias Winkel

We introduce multi-type Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and type and give rise to (size,type)-children in a Galton-Watson fashion, with the rule that…

Probability · Mathematics 2019-12-17 Bénédicte Haas , Robin Stephenson

We show a central limit theorem for random walk on a Galton-Watson tree, when the edges of the tree are assigned randomly uniformly elliptic conductances. When a positive fraction of edges is assigned a small conductance $\varepsilon$, we…

Probability · Mathematics 2024-10-14 Tabea Glatzel , Jan Nagel

The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…

Data Structures and Algorithms · Computer Science 2021-05-26 Svein Høgemo , Benjamin Bergougnoux , Ulrik Brandes , Christophe Paul , Jan Arne Telle

Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…

Statistical Mechanics · Physics 2014-08-25 Yon Visell , Guillaume Millet

We are interested in the biased random walk on a supercritical Galton--Watson tree in the sense of Lyons, Pemantle and Peres, and study a phenomenon of slow movement. In order to observe such a slow movement, the bias needs to be random;…

Probability · Mathematics 2015-03-13 Gabriel Faraud , Yueyun Hu , Zhan Shi

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…

Optimization and Control · Mathematics 2025-05-13 Naum Dimitrieski , Jing Cao , Christian Ebenbauer

Let $T_\lambda$ be a Galton--Watson tree with Poisson($\lambda$) offspring, and let $A$ be a tree property. In this paper, are concerned with the regularity of the function $\mathbb{P}_\lambda(A):= \mathbb{P}(T_\lambda \vdash A)$. We show…

Probability · Mathematics 2019-09-20 Yuval Peres , Andrew Swan

We study contextual stochastic optimization problems, where we leverage rich auxiliary observations (e.g., product characteristics) to improve decision making with uncertain variables (e.g., demand). We show how to train forest decision…

Optimization and Control · Mathematics 2022-03-17 Nathan Kallus , Xiaojie Mao

We consider the branch-length estimation problem on a bifurcating tree: a character evolves along the edges of a binary tree according to a two-state symmetric Markov process, and we seek to recover the edge transition probabilities from…

Computation · Statistics 2025-07-30 David Clancy , Hanbaek Lyu , Sebastien Roch

The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47-66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequate than treewidth as an…

Data Structures and Algorithms · Computer Science 2018-05-16 Eunjung Kim , Sang-il Oum , Christophe Paul , Ignasi Sau , Dimitrios M. Thilikos
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