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math.DS2025
Flexibility versus genericity of phase diagrams of perturbed continuous maps on the Cantor set
Hugo Marsan, Mathieu Sablik
Consider the dynamical system constitued by a continuous function where is a finite alphabet. The perturbed counte…
math-ph2025
Non-Robustness of the Zero-Temperature-Limit Gibbs Measures to Perturbations of the Potential
Léopoldine Gayral, Mathieu Sablik
The robustness of properties of a statistical physics model to slight perturbations in the exact local interactions of the model is a very relevant philosophical question, consider…
nlin.CG2025
A perturbed cellular automaton with two phase transitions for the ergodicity
Hugo Marsan, Mathieu Sablik, Ilkka Törmä
The positive rates conjecture states that a one-dimensional probabilistic cellular automaton (PCA) with strictly positive transition rates must be ergodic. The conjecture has been…