Math Park - 01/20/2018 - Nicolas CURIEN - RANDOM MARKETS AND ELECTRICAL NETWORKS

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Institut Henri Poincaré

Published on Streamed live on Jan 20, 2018
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Nicolas CURIEN - RANDOM WALK AND ELECTRICAL NETWORKS: PROBAS IS CONNECTED Summary: What do a random walk on a graph and a network of electrical resistances have in common? A priori none, but in fact these two objects are very closely linked (via harmonic functions and potential theory). So much so that the "physical" intuition coming from electrical networks makes it easy to demonstrate non-trivial mathematical results on random walks such as Polya's theorem. This deep link also makes it possible to physically understand the (conformal) geometry of a planar graph from the point of view of the random walk and opens up perspectives on the theory of quantum gravity in dimension 2. We will explain these links in detail and illustrate their applications with many examples and simulations. ---------------------------------- You can join us on social networks to follow our news. Facebook: / instituthenripoincare Twitter: / inhenripoincare Instagram: / instituthenripoincare LinkedIn: / 11054846

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