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Course Schedule
Mon Tue Wed Thu Fri
9/1 10.30-12.30 10/1 10.30-12.30
14:30-16:30
13/1 8.30-10.30 14/1 10.30-12.30
14:30-16:30
20/1 8.30-10.30 21/1 10.30-12.30
14:30-16:30
27/1 8.30-10.30 28/1 10.30-12.30 30/1 8.30-10.30
February: 10 hours discussion
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Topic 1 (Alessia Nota, Jan. 9 to 10)
Topic 2 (Stefano Olla, Jan. 13 to 21)
Topic 3: Hydrodynamics for asymmetric simple exclusion (Lu Xu, Jan. 27 to 30)
Abstract
As a typical example of asymmetric attractive system, we study a nearest-neighbour simple exclusion process on periodic lattice with asymmetric jump probability. Different from the symmetric one, nontrivial evolution of the particle density can be observed under the hyperbolic space-time scale, following a quasi-linear conservation law. The key ingredient is an entropy inequality at microscopic level based on the attractiveness.
References
[1] Claude Kipnis, Claudio Landim: Scaling Limits of Interacting Particle Systems (Chapter 8. Hydrodynamic limit of asymmetric attractive processes).
[2] Josef Marek, etc.: Weak and Measure-valued Solutions to Evolutionary PDEs (Chapter 2. Scalar conservation laws).
[3] Fraydoun Rezakhanlou: Hydrodynamic limit for attractive particle systems on Z^d. Comm. Math. Phys. 140 417--448, 1991.
[4] Jozsef Fritz: Entropy pairs and compensated compactness for weakly asymmetric systems. Advanced Stuies in Pure Mathematics 39: Stochastic Analysis on Large Scale Interactive Systems, 143--171, 2004.