主题：Activated Random Walks on ℤ^d

主讲人：Leonardo T Rolla 华磊南 教授（上海纽约大学）

Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main models is that of Activated Random Walks. Long-range effects intrinsic to the conservative dynamics and lack of a simple algebraic structure cause standard tools and techniques to break down. This makes the mathematical study of this model remarkably challenging. Yet, some exciting progress has been made in the last ten years, with of a framework of tools and methods which is finally becoming more structured. In this course we present the existing results and reproduce the techniques developed so far.

Reference: arXiv:1906.05037

时间、地点：

第一次：9月16日 星期一(Monday)9:00—11:00， 一楼报告厅

第二次：9月17日 星期二(Tuesday)15:00—17:00， 南阶

第三次：9月18日 星期三(Wednesday)15:00—17:00， 南阶

第四次：9月19日 星期四(Thursday)9:00—11:00， 南研

第五次：9月20日 星期五(Friday)15:00—17:00 ， 一楼报告厅

主讲人简介：

Education

2008 – PhD in Mathematics. Area: Probability

Institute for Pure and Applied Mathematics - IMPA. Adviser: Vladas Sidoravicius

2004 – Masters in Mathematics. Area: Partial Differential Equations

The Federal University of Minas Gerais - UFMG. Adviser: Gastão Braga

2003 – Bachelor in Computer Mathematics, The Federal University of Minas Gerais

Academic positions

2014-date Visiting Assistant Professor, New York University Shanghai

2012-date Associate Professor, tenured, Argentinian National Research Council

2014-date Associate Professor

2012-2014 Assistant Professor

2010-2012 Excellence post-doctorate, Institute for Pure and Applied Mathematics

2008-2010 Post-doctorate, Fondation Sciences Mathématiques de Paris

École Normale Supérieure de Paris. Supervisor: Wendelin Werner

2008-2008 Post-doctorate, The University of São Paulo. Supervisor: Pablo A. Ferrari

Research articles

L. T. Rolla, V. Sidoravicius, O. Zindy. Universality and Sharpness in Activated Random Walks. Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics 20:1823-1835, 2019.

B. N. B. de Lima, L. T. Rolla, D. Valesin. Monotonicity and Phase Diagram for Multi-Range Percolation on Oriented Trees. Random Structures and Algorithms 55:160-172, 2019.

T. Johnson, L. T. Rolla. Sensitivity of the frog model to initial conditions. Electronic Communications in Probability 24:29, 2019.

M. Cabezas, L. T. Rolla, V. Sidoravicius. Recurrence and Density Decay for Diffusion-Limited

Annihilating Systems. Probability Theory and Related Fields 170:587-615, 2018.

L. T. Rolla, L. Tournier. Non-fixation for Biased Activated Random Walks. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 54:938-951, 2018.

L. T. Rolla, V. Sidoravicius. Stability of the Greedy Algorithm on the Circle. Communications on Pure and Applied Mathematics 70:1961-1986, 2017.

A. Deshayes, L. T. Rolla. Scaling limit of subcritical contact process. Stochastic Processes and their

Applications 127:2630-2649, 2017.

E. Andjel, F. Ezanno, P. Groisman, L. T. Rolla. Subcritical Contact Process Seen from the Edge:

Convergence to Quasi-Equilibrium. Electronic Journal of Probability 20:32, 2015.

R. Markarian, L. T. Rolla, V. Sidoravicius, F. A. Tal, M. E. Vares. Stochastic Perturbations of Convex

Billiards. Nonlinearity 28:4425-4434, 2015.

S. Foss, L. T. Rolla, V. Sidoravicius. Greedy Walk on the Real Line. The Annals of Probability

43:1399-1418, 2015.

P. A. Ferrari, L. T. Rolla. Yaglom Limits via Holley Inequality. Brazilian Journal of Probability and

Statistics 29:413-426 (issue celebrating Errico Presutti’s 70th birthday), 2015.

L. T. Rolla, V. Sidoravicius, L. Tournier. Greedy Clearing of Persistent Poissonian Dust. Stochastic

Processes and their Applications 124:3496-3506, 2014.

M. Cabezas, L. T. Rolla, V. Sidoravicius. Non-equilibrium Phase Transitions: Activated Random Walks at Criticality. Journal of Statistical Physics 155:1112-1125 (issue in honor of Herbert Spohn), 2014.

L. T. Rolla, V. Sidoravicius. Absorbing-State Phase Transition for Driven-Dissipative Stochastic Dynamicson Z. Inventiones Mathematicae 188:127-150, 2012.

M. R. Hilário, O. Louidor, C. M. Newman, L. T. Rolla, S. Sheffield, V. Sidoravicius. Fixation for

Distributed Clustering Processes. Communications on Pure and Applied Mathematics 63:926-

934, 2010.

R. Dickman, L. T. Rolla, V. Sidoravicius. Activated Random Walkers: Facts, Conjectures and Challenges.Journal of Statistical Physics 138:126-142, 2010.

L. T. Rolla, V. Sidoravicius, D. Surgailis, M. E. Vares. The Discrete and Continuum Broken Line Process.Markov Processes and Related Fields 16:79-116, 2010.

L. T. Rolla, A. Q. Teixeira. Last Passage Percolation in Macroscopically Inhomogeneous Media.

Electronic Communications in Probability 13:131-139, 2008.

G. A. Braga, F. Furtado, J. M. Moreira, L. T. Rolla. Renormalization Group Analysis of Nonlinear

Diffusion Equations with Time Dependent Coefficients: Analytical Results. Discrete and Continuous Dynamical Systems. Series B 7:699-715, 2007.

F. M. Q. Pereira, L. T. Rolla, C. G. Rezende, R. L. Carceroni. The Language LinF for Fractal

Specification. In: XVI Brazilian Symposium on Computer Graphics and Image Processing, 2003, São Carlos. Proceedings of the SIBGRAPI 2003:67-74, IEEE, 2003.

G. A. Braga, F. Furtado, J. M. Moreira, L. T. Rolla. Renormalization Group Analysis of Nonlinear

Diffusion Equations with Periodic Coefficients. SIAM Multiscale Modeling and Simulation 1:630-

644, 2003.