Related papers: Distances and large deviations in the spatial pref…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
The paper considers two-phase random design linear regression models. The errors and the regressors are stationary long-range dependent Gaussian. The regression parameters, the scale parameters and the change-point are estimated using a…
Self-attention-based networks have achieved remarkable performance in sequential recommendation tasks. A crucial component of these models is positional encoding. In this study, we delve into the learned positional embedding, demonstrating…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting neurons indexed by a lattice $\mathbb{Z}^d$. The neurons are subject to noise, which is modelled as a correlated martingale. The…
The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context…
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…
This paper models information diffusion in a network of Large Language Models (LLMs) that is designed to answer queries from distributed datasets, where the LLMs can hallucinate the answer. We introduce a two-time-scale dynamical model for…
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…
In the 1960s, the world-renowned social psychologist Stanley Milgram conducted experiments that showed that not only do there exist ``short chains'' of acquaintances between any two arbitrary people, but that these arbitrary strangers are…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
Reciprocity, or the stochastic tendency for actors to form mutual relationships, is an essential characteristic of directed network data. Existing latent space approaches to modeling directed networks are severely limited by the assumption…
We derive distributional approximations for the number of triangles in the linear preferential attachment model $\mathrm{PAM}(m,\delta)$, where $m\ge 2$ and $\delta>-m$, with explicit rates of convergence. The limiting distribution…
A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment,…