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Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…

Machine Learning · Computer Science 2025-03-13 Chengyue Gong , Xiaoyu Li , Yingyu Liang , Jiangxuan Long , Zhenmei Shi , Zhao Song , Yu Tian

In this paper, we study the entropy of a hard random geometric graph (RGG), a commonly used model for spatial networks, where the connectivity is governed by the distances between the nodes. Formally, given a connection range $r$, a hard…

Information Theory · Computer Science 2026-01-19 Praneeth Kumar Vippathalla , Justin P. Coon , Mihai-Alin Badiu

We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…

Statistical Mechanics · Physics 2019-03-06 Francesco Coghi , Jules Morand , Hugo Touchette

In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…

Probability · Mathematics 2007-05-23 Remco van der Hofstad , Gerard Hooghiemstra , Dmitri Znamenski

For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the…

Probability · Mathematics 2021-09-16 Tyler Helmuth , Matthew Jenssen , Will Perkins

Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions $\mathscr L$ that induce a flow, given by $\mathscr L(\rho_t,\dot\rho_t)=0$. We derive necessary and…

Functional Analysis · Mathematics 2018-01-17 Alexander Mielke , D. R. Michiel Renger , Mark A. Peletier

This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…

Probability · Mathematics 2021-03-08 James MacLaurin

We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study…

Probability · Mathematics 2025-09-17 Christian Borgs , Jennifer Chayes , Julia Gaudio , Samantha Petti , Subhabrata Sen

For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number…

Probability · Mathematics 2016-08-16 Kwabena Doku-Amponsah , Peter Mörters

A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…

Deep learning-based fluence map prediction(DL-FMP) method has been reported in the literature, which generated fluence maps for desired dose by deep neural network(DNN)-based inverse mapping. We hypothesized that DL-FMP is similar to…

Medical Physics · Physics 2021-05-03 Lin Ma , Mingli Chen , Xuejun Gu , Weiguo Lu

This work has two contributions. The first one is extending the Large Deviation Principle for uniform hyper-graphons from Lubetzky and Zhao \cite{lubetzky2015replica} to the multi-relational setting where each hyper-graphon can have…

General Mathematics · Mathematics 2024-03-18 Juan Alvarado , Jan Ramon , Yuyi Wang

The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…

Probability · Mathematics 2019-12-12 Shankar Bhamidi , Amarjit Budhiraja , Paul Dupuis , Ruoyu Wu

Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing…

Statistics Theory · Mathematics 2026-03-27 Subhro Ghosh , Rathindra Nath Karmakar , Samriddha Lahiry

We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…

Probability · Mathematics 2026-03-04 Paola Bermolen , Valeria Goicoechea , José R. León

We combine hydrodynamic and modulated energy techniques to study the large deviations of systems of particles with pairwise singular repulsive interactions and additive noise. Specifically, we examine periodic Riesz interactions indexed by…

Probability · Mathematics 2024-08-20 Elias Hess-Childs

We prove the large deviations principle for empirical Bures-Wasserstein barycenters of independent, identically-distributed samples of covariance matrices and covariance operators. As an application, we explore some consequences of our…

Probability · Mathematics 2024-09-18 Adam Quinn Jaffe , Leonardo V. Santoro

Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the…

Probability · Mathematics 2018-01-22 Francis Comets , Gregorio R. Moreno Flores , Alejandro F. Ramirez

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…

Statistical Mechanics · Physics 2009-11-07 Stephane Coulomb , Michel Bauer

Let $H_n$ be a graph on $n$ vertices and let $\ber{H_n}$ denote the complement of $H_n$. Suppose that $\Delta = \Delta(n)$ is the maximum degree of $\ber{H_n}$. We analyse three algorithms for sampling $d$-regular subgraphs ($d$-factors) of…

Combinatorics · Mathematics 2019-10-25 Pu Gao , Catherine Greenhill