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.
