- Department of Mathematics
- University of California
- Berkeley, CA, 94720-3840

The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps (with Alvaro Pelayo)

Kinetic Description of Scalar Conservation Laws with Markovian Data

A Kinetic Approach to Burgers Equation with White Noise Initial Data (with Mehdi Ouaki)

Hamiltonian ODE, Homogenization, and Symplectic Topology , to appear in volume 72 of MSRI Book Series.

Scaling Limit of Small Random Perturbation of Dynamical Systems (with Insuk Seo), Ann. Inst. H. Poincare-Probabilites et Statistiques, vol 59, 869--903 (2023)

Random Tessellations and Gibbsian Solutions of Hamilton-Jacobi Equations (with Mehdi Ouaki)Commun. Math. Phys. vol 394, 409--470 (2022).

Kinetic statistics of scalar conservation laws with piecewise-deterministic Markov process data (with Dave Kaspar) Arch. Rational Mech. Anal. Volume 1, 259--298 (2020).

Stochastic Solutions to Hamilton-Jacobi Equations . In ``Stochastic Dynamics Out of Equilibrium,'' Springer Proceedings in Mathematics and Statistics, Volume 282, 206-238 (2019).

Metastability of Zero Range Processes via Poisson Equations

Optimal Transport Problems For Contact Structures .

Regular Flows for Diffusions with Rough Drifts .

The Poincare--Birkhoff Theorem in Random Dynamics (with A. Pelayo) Trans. Amer. Math. Soc. Volume 370, 601-639 (2018).

Scalar conservation laws with monotone pure-jump Markov initial conditions (with Dave Kaspar) Probab. Theory and Related Fields. volume 165, 867-899 (2016).

Stochastically Symplectic Maps and Their Applications to Navier-Stokes Equation . Ann. Inst. H. Poincare-Anal. Non Lineaire, Volume 33, 1--22 (2016).

Pointwise Bounds for the Solutions of the Smoluchowski Equation with Diffusion,. Arch. Rational Mech. Anal. 212, 1011--1035 (2014).

Gelation for Marcus-Lushnikov Process. This paper (without Section 5) appeared in Annals of Probability, Volume 41, 1806-1830 (2013).

Moment Bounds for the Solutions of the Smoluchowski Equation with Coagulation and Fragmentation, Proceedings of the Royal Society of Edinburgh, Volume 140A, 1041-1059 (2010)

A Prelude to the Theory of Random Walks in Random Environments, Bulletin of IMS, Volume 37, No. 2, 5-20 (2011).

Equilibrium Fluctuations for a Model of Coagulating-Fragmenting planar Brownian Particles, Commun. Math. Phys. Volume 296, 769-826, (2010)

Coagulation, Diffusion and the Continuous Smoluchowski Equation, Stochastic Process. Appl. Volume 119, 3042-3080 , (2009)

Moment bounds for the Smoluchowski equation and their consequences, Commun. Math. Phys. Volume 276, 645-670, (2007)

The kinetic limit of a system of coagulating Brownian particles (with Alan Hammond) Arch. Rational Mech. Anal. Volume 185, 1-67, (2007)

Boltzmann-Grad limits for stochastic hard sphere models Comm. Math. Phys. Volume 284, 555-637 (2004)

Lectures on Symplectic Geometry.

Lectures on Dynamical Systems, part I , part II .

Hamiltonian ODE, Homogenization, and Symplectic Topology.

Lectures on Large Deviation Principle.

Stochastic Growth and KPZ Equation.

Mathematical Methods in Physical Sciences.

Growth Models and Hamilton-Jacobi PDEs.

Equilibrium Fluctuations for Coagulating-Fragmenting Brownian Particles.

Coagulating Brownian Particles, Gelation and Smoluchowski Equation

Kinetic Theory for Hamiton-Jacobi PDE

Kinetic Description for Hamilton-Jacobi Equation: Part I, Part II, Part III, Part IV,

** Editorial Board:
**

- SIAM Journal of Mathematical Analysis 01/2020-present
- Annals of Probability 2015-2021