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pro vyhledávání: '"Thieullen, A."'
In discrete schemes, weak KAM solutions may be interpreted as approximations of correctors for some Hamilton-Jacobi equations in the periodic setting. It is known that correctors may not exist in the almost periodic setting. We show the existence of
Externí odkaz:
http://arxiv.org/abs/2308.13058
Autor:
Privault, Nicolas, Thieullen, Michèle
We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and s
Externí odkaz:
http://arxiv.org/abs/2210.15549
In the following work, we consider the Boltzmann equation that models a polyatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section $\mathcal{B}$, we prov
Externí odkaz:
http://arxiv.org/abs/2208.14343
We construct a finite-range potential on a bidimensional full shift on a finite alphabet that exhibits a zero-temperature chaotic behavior as introduced by van Enter and Ruszel. This is the phenomenon where there exists a sequence of temperatures tha
Externí odkaz:
http://arxiv.org/abs/2208.10346
Autor:
Su, Xifeng, Thieullen, Philippe
Liv\v{s}ic theorem for flows asserts that a Lipschitz observable that has zero mean average along every periodic orbit is necessarily a coboundary, that is the Lie derivative of a Lipschitz function smooth along the flow direction. The positive Liv\v
Externí odkaz:
http://arxiv.org/abs/2205.10135
Publikováno v:
In Advances in Mathematics November 2024 457
Liv\v{s}ic theorem asserts that, for Anosov diffeomorphisms/flows, a Lipschitz observable is a coboundary if all its Birkhoff sums on every periodic orbits are equal to zero. The transfer function is then Lipschitz. We prove a positive Liv\v{s}ic the
Externí odkaz:
http://arxiv.org/abs/2107.08776
Akademický článek
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Autor:
Bandini, Elena, Thieullen, Michele
In this paper we consider the optimal control of Hilbert space-valued infinite-dimensional Piecewise Deterministic Markov Processes (PDMP) and we prove that the corresponding value function can be represented via a Feynman-Kac type formula through th
Externí odkaz:
http://arxiv.org/abs/1906.02250
Autor:
Su, Xifeng, Thieullen, Philippe
Ergodic optimization and discrete weak KAM theory are two parallel theories with several results in common. For instance, the Mather set is the locus of orbits which minimize the ergodic averages of a given observable. In the favorable cases, the obs
Externí odkaz:
http://arxiv.org/abs/1901.07712