arXiv subjects

Sylvain Rubenthaler

Publications and source records attributed to Sylvain Rubenthaler.

21 records · Page 2Linked to original sources

arXiv2007

The convergence to equilibrium of neutral genetic models

This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both for finite and infinite types (or alleles) models. We then analyze the decays to the equilibrium of finite populations in terms of the convergence to stationarity of their first common ancestor. We estimate the Lyapunov exponent of the distribution flows with respect to the total variation norm. We give bounds on these exponents only depending on the stability with respect to mutation of a single individual; they are inversely proportional to the population size parameter.

math.PR↗

arXiv2006

Fast simulated annealing in $\R^d$ and an application to maximum likelihood estimation

Using classical simulated annealing to maximise a function $ψ$ defined on a subset of $\R^d$, the probability $\p(ψ(θ\_n)\leq ψ\_{\max}-ε)$ tends to zero at a logarithmic rate as $n$ increases; here $θ\_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $ψ\_{\max}$ is the maximal value of $ψ$. We propose a modified scheme for which this probability is of order $n^{-1/3}\log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replaced by a more heavy-tailed function, and the system is cooled faster. We also show how the algorithm may be applied to functions that cannot be computed exactly but only approximated, and give an example of maximising the log-likelihood function for a state-space model.

math.PR↗

arXiv2006

Coalescent tree based functional representations for some Feynman-Kac particle models

We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original combinatorial, and permutation group analysis of a special class of forests. They provide refined non asymptotic propagation of chaos type properties, as well as sharp $\LL\_p$-mean error bounds, and laws of large numbers for $U$-statistics. Applications to particle interpretations of the top eigenvalues, and the ground states of Schrödinger semigroups are also discussed.

math.PR↗