Introduction to random Tug-of-War Games and Partial Differential Equations

Juan J. Manfredi (University of Pittsburgh, Pittsburgh, USA)

In this course we present an introduction to the results of Peres, Schramm, Sheffield and Wilson [Journal of the American Mathematical Society, 22(1):167-210, 2009] and Peres and Sheffield [Duke Math Journal, 145, 1 (2008), 91-120] on random Tug-of-War games, the ∞-Laplace operator and the p-Laplace operator. A tentative program is as follows:

• Probabilistic background (Kolmogorov theorem and Martingales).
• Game Theory background (Two-person zero-sum games).
• PDE background (The p-Laplacian for 1<p≤∞).
• ∞-harmonious and p-harmonious functions.