Networks of reinforced stochastic processes: a complete description of the first-order asymptotics
G Aletti, I Crimaldi, A Ghiglietti - Stochastic Processes and their …, 2024 - Elsevier
We consider a finite collection of reinforced stochastic processes with a general network-
based interaction among them. We provide sufficient and necessary conditions for the …
based interaction among them. We provide sufficient and necessary conditions for the …
A finite memory interacting Pólya contagion network and its approximating dynamical systems
We introduce a new model for contagion spread using a network of interacting finite memory
two-color Pólya urns, which we refer to as the finite memory interacting Pólya contagion …
two-color Pólya urns, which we refer to as the finite memory interacting Pólya contagion …
Urns with Multiple Drawings and Graph-Based Interaction
Y Dahiya, N Sahasrabudhe - Journal of Theoretical Probability, 2024 - Springer
Consider a finite undirected graph and place an urn with balls of two colours at each vertex.
At every discrete time step, for each urn, a fixed number of balls are drawn from that same …
At every discrete time step, for each urn, a fixed number of balls are drawn from that same …
Elephant random walks with graph based shared memory: First and second order asymptotics
D Das - arXiv preprint arXiv:2410.22969, 2024 - arxiv.org
We consider a generalization of the so-called elephant random walk by introducing multiple
elephants moving along the integer line, $\mathbb {Z} $. When taking a new step, each …
elephants moving along the integer line, $\mathbb {Z} $. When taking a new step, each …
Interacting urn models with strong reinforcement
S Qin - arXiv preprint arXiv:2311.13480, 2023 - arxiv.org
We disprove a conjecture by Launay that almost surely one color monopolizes all the urns
for the interacting urn model with polynomial reinforcement and parameter $ p> 0 …
for the interacting urn model with polynomial reinforcement and parameter $ p> 0 …
Feedback interacting urn models
We introduce and discuss a special type of feedback interacting urn model with deterministic
interaction. This is a generalisation of the very well known Eggenberger and Polya (1923) …
interaction. This is a generalisation of the very well known Eggenberger and Polya (1923) …
Urns with Multiple Drawings and Graph-Based Interaction
Y Dahiya, N Sahasrabudhe - arXiv preprint arXiv:2308.12528, 2023 - arxiv.org
Consider a finite undirected graph and place an urn with balls of two colours at each vertex.
At every discrete time step, for each urn, a fixed number of balls are drawn from that same …
At every discrete time step, for each urn, a fixed number of balls are drawn from that same …
Existence and Convergence of Interacting Particle Systems on Graphs
KG Mazumder - arXiv preprint arXiv:2408.07976, 2024 - arxiv.org
We give a general existence and convergence result for interacting particle systems on
locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state …
locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state …
Networks of reinforced stochastic processes: Probability of asymptotic polarization and related general results
G Aletti, I Crimaldi, A Ghiglietti - Stochastic Processes and their …, 2024 - Elsevier
In a network of reinforced stochastic processes, for certain values of the parameters, all the
agents' inclinations synchronize and converge almost surely toward a certain random …
agents' inclinations synchronize and converge almost surely toward a certain random …
Interacting Urns on Directed Networks with Node-Dependent Sampling and Reinforcement
G Kaur, N Sahasrabudhe - arXiv preprint arXiv:2312.02096, 2023 - arxiv.org
We consider interacting urns on a finite directed network, where both sampling and
reinforcement processes depend on the nodes of the network. This extends previous …
reinforcement processes depend on the nodes of the network. This extends previous …