Stochastic Dynamics Out of Equilibrium: Institut Henri Poincaré, Paris, France, 2017 (Springer Proceedings in Mathematics & Statistics Book 282)

Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas. Front Matter ....Pages i-xi Front Matter ....Pages 1-1 Stochastic Mean-Field Dynamics and Applications to Life Sciences (Paolo Dai Pra)....Pages 3-27 Alignment of Self-propelled Rigid Bodies: From Particle Systems to Macroscopic Equations (Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno, Ariane Trescases)....Pages 28-66 Fluctuations in Stochastic Interacting Particle Systems (Gunter M. Schütz)....Pages 67-134 Front Matter ....Pages 135-135 Hydrodynamics for Symmetric Exclusion in Contact with Reservoirs (Patrícia Gonçalves)....Pages 137-205 Stochastic Solutions to Hamilton-Jacobi Equations (Fraydoun Rezakhanlou)....Pages 206-238 Front Matter ....Pages 239-239 On Optimal Decay Estimates for ODEs and PDEs with Modal Decomposition (Franz Achleitner, Anton Arnold, Beatrice Signorello)....Pages 241-264 Adaptive Importance Sampling with Forward-Backward Stochastic Differential Equations (Omar Kebiri, Lara Neureither, Carsten Hartmann)....Pages 265-281 Ergodic Properties of Quasi-Markovian Generalized Langevin Equations with Configuration Dependent Noise and Non-conservative Force (Benedict Leimkuhler, Matthias Sachs)....Pages 282-330 Exit Event from a Metastable State and Eyring-Kramers Law for the Overdamped Langevin Dynamics (Tony Lelièvre, Dorian Le Peutrec, Boris Nectoux)....Pages 331-363 Collisional Relaxation and Dynamical Scaling in Multiparticle Collisions Dynamics (Stefano Lepri, Hugo Bufferand, Guido Ciraolo, Pierfrancesco Di Cintio, Philippe Ghendrih, Roberto Livi)....Pages 364-374 A Short Introduction to Piecewise Deterministic Markov Samplers (Pierre Monmarché)....Pages 375-390 Time Scales and Exponential Trend to Equilibrium: Gaussian Model Problems (Lara Neureither, Carsten Hartmann)....Pages 391-410 Front Matter ....Pages 411-411 Stochastic Models of Blood Vessel Growth (Luis L. Bonilla, Manuel Carretero, Filippo Terragni)....Pages 413-436 Survival Under High Mutation (Rinaldo B. Schinazi)....Pages 437-442 Particle Transport in a Confined Ratchet Driven by the Colored Noise (Yong Xu, Ruoxing Mei, Yongge Li, Jürgen Kurths)....Pages 443-456 Long-Time Dynamics for a Simple Aggregation Equation on the Sphere (Amic Frouvelle, Jian-Guo Liu)....Pages 457-479 Front Matter ....Pages 481-481 Tracy-Widom Asymptotics for a River Delta Model (Guillaume Barraquand, Mark Rychnovsky)....Pages 483-522 Hydrodynamics of the N-BBM Process (Anna De Masi, Pablo A. Ferrari, Errico Presutti, Nahuel Soprano-Loto)....Pages 523-549 1D Mott Variable-Range Hopping with External Field (Alessandra Faggionato)....Pages 550-559 Invariant Measures in Coupled KPZ Equations (Tadahisa Funaki)....Pages 560-568 Reversible Viscosity and Navier–Stokes Fluids (Giovanni Gallavotti)....Pages 569-580 On the Nonequilibrium Entropy of Large and Small Systems (Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Pablo Sartori)....Pages 581-596 Marginal Relevance for the \(\gamma \)-Stable Pinning Model (Hubert Lacoin)....Pages 597-616 A Rate of Convergence Result for the Frederickson-Andersen Model (Thomas Mountford, Glauco Valle)....Pages 617-620 Stochastic Duality and Eigenfunctions (Frank Redig, Federico Sau)....Pages 621-649 Part I: Mini-courses of the pre-school at CIRM, P. Dai Pra, Stochastic mean-field dynamics and applications to life sciences -- P. Degond*, A. Frouvelle, S. Merino-Aceituno and A. Trescases, Alignment of self-propelled rigid bodies: from particle systems to macroscopic equations -- G. Schütz, Fluctuations in Stochastic Interacting Particle Systems -- Part II: Mini-courses at IHP, P. Gonçalves, Hydrodynamics for symmetric exclusion in contact with reservoirs -- F. Rezakhanlou, Stochastic Solutions to Hamilton-Jacobi Equations -- Part III: Workshop 1: Numerical aspects of nonequilibrium dynamics, F. Achleitner, A. Arnold* and B. Signorello, On Optimal Decay Estimates for ODEs and PDEs with Modal Decomposition -- O. Kebiri, L. Neureither and C. Hartmann*, Adaptive importance sampling with forward-backward stochastic differential equations -- B. Leimkuhler* and M. Sachs, Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force -- T. Lelièvre, Dorian Le Peutrec and B. Nectoux*, Exit event from a metastable state and Eyring-Kramers law for the overdamped Langevin dynamics -- S. Lepri, Collisional relaxation and dynamical scaling in multiparticle collisions dynamics -- P. Monmarché, A short introduction to Piecewise Deterministic Markov samplers -- L. Neureither and C. Hartmann*, Time scales and exponential trend to equilibrium: Gaussian model problems -- Part IV: Workshop 2: Life sciences, L. L. Bonilla*, M. Carretero and F. Terragni, Stochastic models of blood vessel growth -- R. Schinazi, Survival under high mutation -- Y. Xu, R. Mei, Y. Li and J. Kurths*, Particle transport in a confined ratchet driven by the colored noise -- A. Frouvelle* and Jian-Guo Liu, Long-time dynamics for a simple aggregation equation on the sphere -- Part V: Workshop 3: Stochastic dynamics out of equilibrium, G. Barraquand* and M. Rychnovsky, Tracy-Widom asymptotics for a river delta model -- A. De Masi*, P.A. Ferrari, E. Presutti and N. Soprano-Loto, Hydrodynamics of the N-BBM process -- A. Faggionato, 1D Mott variable-range hopping with external field -- T. Funaki, Invariant measures in coupled KPZ equations -- G. Gallavotti, Reversible Viscosity and Navier-Stokes Fluids -- S. Goldstein, D. Huse, J. Lebowitz* and P. Sartori, On the nonequilibrium entropy of large and small systems -- H. Lacoin, Marginal relevance for the $ gamma$-stable pinning model -- T. Mountford* and Glauco Valle, A rate of convergence result for the Frederickson-Andersen model -- F. Redig* and F. Sau, Stochastic duality and eigenfunctions Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph. D. students working in such areas.-- Provided by publisher "Stemming from the IHP trimester Stochastic Dynamics Out of Equilibrium, this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas"--Page 4 of cover Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph. D. students working in such areas