Title：Potential theory and combinatorics
Speaker：Sami Mustapha(Sorbonne Université)
Time：Friday, October27,16:15-17:15
Location：Mingde Building, B201-1
Abstract：“... But the most general and direct method for resolving questionsof probability consists of making them depend on difference equations ...”
The aim of this talk is to illustrate this quote from Laplace (Philosophical essayon probabilities) by developing certain aspects of the theory of discretepotential theory attached to a random walk in; the difference equationsplaying in this framework the same role played by the PDEs in the theory ofthe classical potential theory. Although the presentation will be mainly limitedto simple walks in quadrants, some extensions to walks in discrete Lipschitziandomains and to inhomogeneous walks will be discussed. The emphasis will beplaced on the role that tools from discrete potential theory can play (harmonicfunctions and discrete caloric functions, maximum principle, Harnackinequalities, boundary Harnack inequalities at the boundary) in establishingoptimal estimates for the number of paths confined to a region as well as thenumber of excursions.
About the speaker:
Sami Mustapha现任法国索邦大学教授，数学学院院长。Sami Mustapha教授是世界著名调和分析专家，在群上的调和分析及随机游走等领域作出了杰出贡献。
More information aboutDistinguished Colloquiumcan be foundhere.
