169 citations · 527 across the 30 of their papers we have counts for
5 papers · 2 filters
A generalized Polya's urn with graph based interactions
Michel Benaim, Itai Benjamini, Jun Chen +1
Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a p…
Strongly Vertex-Reinforced-Random-Walk on the complete graph
Michel Benaïm, Olivier Raimond, Bruno Schapira
We study Vertex-Reinforced-Random-Walk on the complete graph with weights of the form , with . Unlike for the Edge-Reinforced-Random-Walk, which in this case localiz…
On the stability of planar randomly switched systems
Michel Benaïm, Stéphane Le Borgne, Florent Malrieu +1
Consider the random process (Xt) solution of dXt/dt = A(It) Xt where (It) is a Markov process on {0,1} and A0 and A1 are real Hurwitz matrices on R2. Assuming that there exists lam…
Qualitative properties of certain piecewise deterministic Markov processes
Michel Benaïm, Stéphane Le Borgne, Florent Malrieu +1
We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field th…
Quantitative ergodicity for some switched dynamical systems
Michel Benaïm, Stéphane Le Borgne, Florent Malrieu +1
We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd \times E where E is a finite set. The continuou…