Probability in Mathematical Physics and Computational Physics.
Analysis of Interacting Particle Systems
Splitting (birth\death of replicas) methods for rare event simulation. Fleming-Viot particle systems (P2,P3,15,14,13).
Large time behavior of Kac's particle system (P1).
Large time behavior of Feynman-Kac particle systems. The "sign problem" for Fermions (2,9).
Adaptive bias (6,5).
Splitting (birth\death of replicas) methods for Gibbs sampling (10,4,3,M1).
Randomly Perturbed Mechanical Systems (P4,10,8,7,4,M1).
Stochastic analysis of kinetic models in biology (11,12).
(i)-In this simulation with periodic boundary conditions, a dimer (in red) is coupled to a simple model for solvant (in green). The slow degree of freedom (reaction coordinate) is the distance between the two atoms of the dimer, and has two different stable configurations (blue or red). The fast degrees of freedom comes from the motion of the atoms of the solvant (in green). In a second simulation, an adaptive biasing technique is used to accelerate the transition between configurations (between blue and red) of the dimer (references: (10), (6), and (5)).
(ii)-In this simulation, we simulate a large polymeric chain of atoms attached at one hand and coupled to a thermostat. Bonds, and bond angles between atoms are rigid, and the time step is limited by the fast oscillation of the torsion angles. In a second simulation, the oscillation of torsion angles are correlated, using an implicit mass-matrix penalty which does not modify the probability distribution of the different configurations of the system. It results in larger time steps, and in an accelerated simulation (references: (8)).
HdR (Habilitation à Diriger des Recherches):
Title of dissertation: "Probability in Computational Physics and Biology: some mathematical contributions". HdR dissertation.
HdR defense slides.
Title of dissertation: "Continuous time "Population Monte Carlo" and Computational Physics".
PhD advisors: Pierre Del Moral and Laurent Miclo. PhD dissertation.
Preprints (P4) Mathias Rousset, Pierre-André Zitt, Yushun Xu: A Weak Overdamped Limit Theorem for Langevin Processespdf (P3) Fréderic Cérou, Bernard Delyon, Arnaud Guyader, Mathias Rousset: A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killingpdf (P2) Fréderic Cérou, Bernard Delyon, Arnaud Guyader, Mathias Rousset: A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killingpdf (P1) Mathias Rousset: A N-uniform quantitative Tanaka's theorem for the conservative Kac's N-particle system with Maxwell molecules.pdf
Published articles (15) Henri Louvin, Eric Dumonteil, Tony Lelièvre, Mathias Rousset and Cheikh M. Diop (2017): Adaptive multilevel splitting for Monte Carlo particle transport EPJ Nuclear Sci. Technol. 3, 29 pdf (14) C.E. Brehier, M Gazeau, L. Goudenège and M.Rousset (2016): Unbiasedness of some generalized Adaptive Multilevel Splitting algorithms Ann. Appl. Prob. pdf (13) C.E. Brehier, T. Lelièvre and M.Rousset (2015): Analysis of Adaptive Multilevel Splitting algorithms in an idealized case. ESAIM P&S, to appear pdf (12) M.Rousset and G.Samaey (2013): Simulating individual-based models of bacterial chemotaxis with asymptotic variance reduction. M3AS, 23:2155-2191. pdf (11) M.Rousset and G.Samaey (2013): Individual-based models for bacterial chemotaxis in the diffusion asymptotics. M3AS, 23:2005-2037. pdf (10) T. Lelièvre, M. Rousset and G. Stoltz (2012): Langevin dynamics with constraints and computation of free energy differences. Maths of Comp. 81, p 2071-2125: (Preprint pdf) (9) M.Rousset (2010): On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes. M2AN, Vol. 44, Issue 5, p 977-995. (Preprint version: pdf) (8) P. Plechac and M. Rousset (2009): Implicit Mass-Matrix Penalization of Hamiltonian dynamics with application to exact sampling of stiff systems. SIAM MMS, 8, No 2, arXiv:0805.1092. (7) T. Goudon and M. Rousset (2009): Stochastic Acceleration in an Inhomogeneous Time Random Force Field. Appl Math Res Express. 2009: 1-46 (Preprint version: pdf ) (6) T. Lelièvre, M. Rousset and G. Stoltz (2008): Long time convergence of the Adaptive Biaising Force method. Nonlinearity, 21, 1155-1181 (Preprint version: pdf) (5) T.Lelièvre, M.Rousset and G.Stoltz (2007): Computation of free energy differences with parallel adaptive dynamics . J. Chem. Phys, Vol.126, No.13. (Preprint version: pdf) (4) T.Lelièvre, M.Rousset and G.Stoltz (2007): Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case. J. Comp. Phys. 222(2), 624-643. (Preprint version: pdf) (3) M.Rousset and G.Stoltz (2006): Equilibrium sampling from nonequilibrium dynamics. J. Stat. Phys., 123 (6), 1251-1272. (Preprint version: pdf) (2) M.Rousset (2006): On the control of an interacting particle approximation of Schrödinger ground states. SIAM J. Math. Anal., 38 (3), 824-844.(Preprint version: pdf) (1) M.Rousset (2004): Sur la rigidité de polyèdres hyperboliques en dimension 3: cas de volume fini, cas hyperidéal, cas fuchsien. Bull. SMF 132, 233-261. (Preprint version: pdf)
Monographs (M1) T.Lelièvre, M.Rousset and G.Stoltz (2010): Free energy computation: a mathematical perspective. Imperial College Press
Proceedings and miscellaneous (C2)-C.E. Brehier, M Gazeau, L. Goudenège and M.Rousset (2014): Analysis and simulation of rare events for SPDE. CEMRACS 2014 pdf (C1)-A.Doucet and M.Rousset (2006): Discussion of "Exact and computationnally efficient likelihood estimation of discretely observed diffusions" (by Beskos and co.). J. Roy. Stat. Soc. B. 68, 333. (Preprint version: pdf)