activity
20132022
most citedStationary measures and phase transition for a class of probabilistic cellular automata

31 citations · 85 across the 10 of their papers we have counts for

collaborators

11 papers

math.ST2022

Statistical test for an urn model with random multidrawing and random addition

Irene Crimaldi, Pierre-Yves Louis, Ida G. Minelli

We complete the study of the model introduced in [11]. It is a two-color urn model with multiple drawing and random (non-balanced) time-dependent reinforcement matrix. The number o…

math.PR2021

Urn models with random multiple drawing and random addition

Irene Crimaldi, Pierre-Yves Louis, Ida Germana Minelli

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…

math.PR2020★ 1 cited

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

Irene Crimaldi, Pierre-Yves Louis, Ida Germana Minelli

'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 ? Interac…

math.PR2016★ 31 cited

Stationary measures and phase transition for a class of probabilistic cellular automata

Paolo Dai Pra, Pierre-Yves Louis, Sylvie Roelly

We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transiti…

math.PR2016★ 15 cited

Ergodicity of PCA: Equivalence between Spatial and Temporal Mixing Conditions

Pierre-Yves Louis

For a general attractive Probabilistic Cellular Automata on S Z d , we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fas…

math.PR2016★ 4 cited

Realizable monotonicity for continuous-time Markov processes

Paolo Dai Pra, Pierre-Yves Louis, Ida Minelli

We formalize and analyze the notions of stochastic monotonicity and realizable mono-tonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set.…

math.PR2016

Monotonicity and complete monotonicity for continuous-time Markov chains

Paolo Dai Pra, Pierre-Yves Louis, Ida Minelli

We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in…

math.PR2016★ 2 cited

Increasing coupling of probabilistic cellular automata

Pierre-Yves Louis

We give a necessary and sufficient condition for the existence of an increasing coupling of () synchronous dynamics on (PCA). Increasing means the co…

math.PR2016★ 22 cited

Synchronization via interacting reinforcement

Paolo Dai Pra, Pierre-Yves Louis, Ida G. Minelli

We consider a system of urns of Polya-type, with balls of two colors; the reinforcement of each urn depends both on the content of the same urn and on the average content of all ur…

math.PR2016

Synchronization and functional central limit theorems for interacting reinforced random walks

Irene Crimaldi, Paolo Dai Pra, Pierre-Yves Louis +1

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 re…

cond-mat.stat-mech2013★ 10 cited

Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible Probabilistic Cellular Automata

Emilio N. M. Cirillo, P. -Y. Louis, W. M. Ruszel +1

Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generaliza…