Related papers: Internal Diffusion Limited Aggregation on discrete…
In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…
Federated Learning (FL) offers a decentralized approach to model training, where data remains local and only model parameters are shared between the clients and the central server. Traditional methods, such as Federated Averaging (FedAvg),…
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…
In this work, we demonstrate that a functional modeling the self-aggregation of stochastically distributed lipid molecules can be obtained as the $\Gamma$-limit of a family of discrete energies driven by a sequence of independent and…
A microscopic model of the effect of unbinding in diffusion limited aggregation based on a cellular automata approach is presented. The geometry resembles electrochemical deposition - ``ions'' diffuse at random from the top of a container…
In the present note we analyze the one-dimensional multi-particle diffusion limited aggregation (MDLA) model: the initial number of particles at each positive integer site has Poisson distribution with mean $\mu$, independently of all other…
An analytical renormalization group treatment is presented of a model which, for one value of parameters, is equivalent to diffusion limited aggregation. The fractal dimension of DLA is computed to be 2-1/2+1/5=1.7. Higher multifractal…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$…
Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…
Haynes et al. (1977) derived a nonlinear differential equation to determine the spread of innovations within a social network across space and time. This model depends upon the imitators and the innovators within the social system, where…
We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
A common theme underlying many problems in statistics and economics involves the determination of a systematic method of selecting a joint distribution consistent with a specified list of categorical marginals, some of which have an ordinal…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm which makes local moves by incorporating information about the gradient of the logarithm of the target density. In this paper we study the efficiency of MALA on a…
We consider the diffusion of two alternatives in social networks using a game-theoretic approach. Each individual plays a coordination game with its neighbors repeatedly and decides which to adopt. As products are used in conjunction with…