arXiv subjects

Ida Germana Minelli

Publications and source records attributed to Ida Germana Minelli.

7 recordsLinked to original sources

arXiv2025

Reinforced dynamics for interacting agents in competitive or cooperative environments

We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we prove almost sure convergence of agents' states, with bipartite graphs leading to non-deterministic limits and non-bipartite graphs to deterministic ones. These results are extended to reducible networks with cooperative or competitive substructures, using a hierarchical graph representation in which higher-level agents perceive lower-level agents as forcing inputs. A general framework for interacting agents under external forcing is also provided, offering a rigorous characterization of long-term behavior and synchronization phenomena in such systems.

math.PR↗

arXiv2021

Urn models with random multiple drawing and random addition

We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has general random entries. For the proportion of balls of a given color, we prove almost sure convergence results and fluctuation theorems (through CLTs in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution). Asymptotic confidence intervals are given for the limit proportion, whose distribution is generally unknown.

math.PR↗

arXiv2020

Interacting non-linear reinforced stochastic processes: synchronization and no-synchronization

'Rich get richer' rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered in many papers, where the asymptotic behavior was proven to exhibit a.s. synchronization. We consider in this paper models where, even if interaction among agents is present, absence of synchronization may happen due to the choice of an individual non-linear reinforcement. We show how these systems can naturally be considered as models for coordination games, technological or opinion dynamics.

math.PR↗

arXiv2020

Delay-induced periodic behavior in competitive populations

We study a model of binary decisions in a fully connected network of interacting agents. Individual decisions are determined by social influence, coming from direct interactions with neighbours, and a group level pressure that accounts for social environment. In a competitive environment, the interplay of these two aspects results in the presence of a persistent disordered phase where no majority is formed. We sow how the introduction of a delay mechanism in the agent's detection of the global average choice may drastically change this scenario, giving rise to a coordinated self sustained periodic behaviour.

math.PR↗

arXiv2017

Stochastic monotonicity from an Eulerian viewpoint

Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling compatible with respect to the partial order. We consider the case of a countable set and introduce the class of \emph{finitely decomposable flows} on a directed acyclic graph associated to the partial order. We show that a probability measure stochastically dominates another probability measure if and only if there exists a finitely decomposable flow having divergence given by the difference of the two measures. We illustrate the result with some examples. In fluid theory the Lagrangian description follows the trajectories of the particles while the Eulerian one observes the local flow. A coupling gives a Lagrangian description of the transference plan of mass while a flow gives an Eulerian one

math.PR↗

arXiv2016

Synchronization and functional central limit theorems for interacting reinforced random walks

We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are correlated, forcing their convergence to the same, possibly random, limit. Random walks of this form have been introduced in the context of urn models and in stochastic approximation. We also propose an application to opinion dynamics in a random network evolving via preferential attachment. We study, in particular, random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. Under certain conditions, synchronization is faster than convergence.

math.PR↗

arXiv2015

Fluctuation Theorems for Synchronization of Interacting Polya's urns

We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter $α$ in [0,1]; in particular, for $α=0$ the N urns behave as N independent Polya's urns. As shown in [9], for $α>0$ urns synchronize, in the sense that the fraction of balls of a given color converges a.s. to the same (random) limit in all urns. In this paper we study fluctuations around this synchronized regime. The scaling of these fluctuations depends on the parameter $α$. In particular the standard scaling $t^{-1/2}$ appears only for $α>1/2$. For $α\geq 1/2$ we also determine the limit distribution of the rescaled fluctuations. We use the notion of stable convergence, which is stronger than convergence in distribution.

math.PR↗