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Ergodicity of some probabilistic cellular automata with two letters alphabet via random walks
Jérôme Casse
Ergodicity of probabilistic cellular automata is a very important issue in the PCA theory. In particular, the question about the ergodicity of all PCA with two-size neighbourhood,…
Iterated Brownian motion ad libitum is not the pseudo-arc
Jérôme Casse, Nicolas Curien
We show that the construction of a random continuum from independent two-sided Brownian motions as considered in arXiv:2004.01367 almost surely yields a non-degenerat…
Generalised directed last passage percolation: invariant laws on the cylinders
Jérôme Casse
The directed last passage percolation (LPP) on the quarter-plane is a growing model. To come into the growing set, a cell needs that the cells on its bottom and on its left to be i…
Probabilistic cellular automata with memory two: invariant laws and multidirectional reversibility
Jérôme Casse, Irène Marcovici
We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time is drawn according to a d…
Processes iterated ad libitum
Jérôme Casse, Jean-François Marckert
Consider the th iterated Brownian motion . Curien and Konstantopoulos proved that for any distinct numbers , $(I^{(n)}(t_1),\dots,I…