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Optimal Surviving Strategy for the “Up the River” Problem

Seminar: Probability Seminar | March 1 | 3:10-4 p.m. | 1011 Evans Hall

Wenpin Tang, U.C. Berkeley

Department of Statistics

The "Up the River" problem was formulated by Aldous (2002), where a unit drift is distributed among a finite collection of Brownian particles on R+, which are annihilated once they reach the origin. Starting K particles at x = 1, we prove Aldous’ conjecture that the push-the-laggard strategy of distributing the drift asymptotically (as K → ∞) maximizes the total number of surviving particles, with approximately √ 4 π K1/2 surviving particles. The push-the-laggard strategy is closely related to Atlas model, developed by Fernholz, Karatzas, . . .The hydrodynamic limit of the particle density satisfies a two-phase PDE with a moving boundary. (Joint work with Li-Cheng Tsai.)