31 citations · 85 across the 10 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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.…
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…
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…
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…
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…