Theoretical Statistics and Mathematics Unit, ISI Delhi

February 15, 2012 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Ofer Zeitouni,
Weizmann Institute of Science, Israel

Title:
Random Walks

Abstract of Talk

Consider a random walker on a lattice, that at each time step jumps to one of the neighbors with equal probability. It goes back to work of Polya that in dimension 2, the walker surely returns to its starting point, whereas this is false in higher dimension. Further, the scaling limit of the trajectory of the walk is Brownian motion.
None of these statements is known in general when the walk is inhomogeneous in space, with transition probabilities being themselves random. In the talk I will review the classical theory, explain the challenges in the random environment setup, and describe some recent progress. The role played by dimension will be emphasized throughout the talk. No prior knowledge of random walks will be assumed.