Seminar | February 5 | 3:30-5 p.m. | 3108 Etcheverry Hall
Wenpin Tang, UCLA
Nowadays there are more and more people living on the planet, but the available resources are very limited. So an interesting question is how to allocate the limited resources to maximize our welfare.
In this talk, I will present the "Up the River problem" which is a dynamic allocation model in a random environment with limited resources. The model was introduced by David Aldous in 2000, along with a couple of open problems. 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 solution to the problem relies on stochastic calculus and partial differential equations: the hydrodynamic limit of the particle density satisfies a two-phase partial differential equations, one with a fix boundary and the other with a free boundary.
At the end of the talk, I will discuss recent progress in continuous-time information search model, initiated by Ke and Villas-Boas. The techniques in solving the "Up the River problem" can also be applied to these search models. The talk is based on joint work with Li-Cheng Tsai (Up the River problem), Tony Ke and J.Miguel Villas-Boas
Bio: Wenpin Tang is an Assistant Professor at Department of Mathematics, UCLA. He obtained his Ph.D. from Department of Statistics, UC Berkeley. His advisor was Jim Pitman. Before coming to Berkeley, he obtained an engineer diploma (Diplôme d'ingénieur) from Ecole Polytechnique, France.
Research: Tang's research interests include probability theory and its applications. He has been working on paths embedding in Brownian motion (with Jim Pitman), and paths intersection of Brownian motion (with Steve Evans and Jim Pitman). He also solved a conjecture of David Aldous on Up the River problem (with Li-Cheng Tsai).
More generally, he is interested in topics such as random combinatorial objects, stochastic differential equations, and interacting particle systems.
More information can be found on his website here: http://www.math.ucla.edu/~wenpintang/