Noticias en español
Maker-Breaker games on Galton-Watson tres.
Resumen: Maker-Breaker is a classical combinatorial game in which one player fixates, the other one removes edges (taking turns) in order to connect/isolate nodes. This two-player game is considered on the random board given by the family tree of a supercritical Galton-Watson branching proces Strategies and success probabilities are assessed for different levels of information, the players receive during play.
Read MoreSpeciation induced by dormancy in a model with changing environment.
Resumen: We consider a population model in which the season alternates between winter and summer. Individuals can acquire mutations that are advantageous in the summer but disadvantageous in the winter, or vice versa. Furthermore, it is assumed that individuals within the population can either be active or dormant, and that individuals can transition between these two states. Dormant individuals do not reproduce and are not subject to selective pressures. Our findings indicate that, under some conditions, two waves of adaptation emerge over time. Some individuals repeatedly acquire...
Read MoreComparison of arm exponents in planar FK-percolation.
Resumen: FK-percolation is a generalisation of Bernoulli percolation that was found to be related to a wide range of other models in statistical mechanics, including the Ising model and the six-vertex model. In this talk, we will focus on the specific case of critical planar FK-percolation in the continuous phase transition regime. In this setting, the model exhibits properties similar to those of critical planar Bernoulli percolation; in particular, the Russo-Seymour-Welsh theory applies and the model is conjectured to be conformally invariant. Conformal invariance would imply that the...
Read MoreCellular automata and Percolation on groups.
Resumen: a classical theorem of Gilman shows that every cellular automaton over the integers satisfies a strong dichotomy with respect to any iid Bernoulli process: either almost all configurations are sensitive to initial conditions or it is almost everywhere equicontinuous. If instead of the integers we consider an arbitrary finitely generated group, we will show that there is a strong connection between the triviality of the percolation threshold and the validity of this dichotomy. Using this connection, we will show that Gilman’s dichotomy holds on a countable group if and only if...
Read MoreA (dis)continuous percolation phase transition on the hierarchical lattice.
Abstract: For long-range percolation on $\mathbb{Z}$ with translation-invariant edge kernel $J$, it is a classical theorem of Aizenman and Newman (1986) that the phase transition is discontinuous when $J(x-y)$ is of order $|x-y|^{-2}$ and that there is no phase transition at all when $J(x-y)=o(|x-y|^{-2})$. We prove analogous theorems for the hierarchical lattice, where the relevant threshold is at $|x-y|^{-2d} \log \log |x-y|$ rather than $|x-y|^{-2}$: There is a continuous phase transition for kernels of larger order, a discontinuous phase transition for kernels of exactly this order,...
Read MoreLong time asymptotics for critical birth and death diffusion processes.
Resumen: We study the long time behavior for the distribution of a critical birth and death diffusion process, motivated by population dynamics in changing environment (cf. a recent paper by Calvez, Henry, Méléard, Tran). The birth rates are bounded but death rates are unbounded. Our analysis is based on the spectral properties of the associated Feynman Kac semigroup. We require a standard spectral gap property for this semigroup with a dominant eigenfunction vanishing at infinity. Some examples of diffusions, diffusions with jump, pure jump dynamics are given for which it is true....
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