Opening lecture

Prof Takis Konstantopoulos (University of Liverpool) - Stochastic Networks as a gate to theoretical and applied probability

In studying stochastic networks, we see probability (and mathematics) through a certain point of view. This can be exploited in understanding some fundamental and other interesting results in probability theory per se. For example, the ergodic theorem is intimately related to the famous Loynes scheme; the basic theorem of differentiation of measures on the real line is related to the Skorokhod reflection; and so does the Hahn-Jordan decomposition of signed measures; and the ballot theorem is Little's law in disguise. I'll explain these things among others and hope to convey the fascinating process of interaction between theory and research in an applied area.

Closing lecture

Prof Pablo Ferrari (University of Buenos Aires) - TASEP Hydrodynamics using microscopic characteristics

It is known that the rescaled one-dimensional TASEP density fields approach the solution of the unviscid Burgers equation. I will review these results and show a new proof of the limit in the rarefaction fan case using coupling and second class particles. In particular I show how second class particles mimic at the microscopic level the role of (macroscopic) characteristic lines of the equation. The approach is self contained and avoids the sub-additive ergodic theorem which is the crucial tool in the original proof of Hermann Rost.

References:

Pablo A. Ferrari. TASEP hydrodynamics using microscopic characteristics. Probability Surveys, 15:1-27, 2018. arXiv/1601.05346.

Hermann Rost. Nonequilibrium behaviour of a many particle process: density profile and local equilibria. Z. Wahrsch. Verw. Gebiete, 58(1):41-53, 1981.