The University of Arizona
Please note that this event has ended!

Systems of equations driven by fast-oscillating functions of a Wiener process

Mathematical Physics and Probability Seminar

Systems of equations driven by fast-oscillating functions of a Wiener process
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Janek Wehr, University of Arizona

Several applied problems lead to systems of differential equations in the plane, where random terms appear with singular coefficients. Examples are motion of a light-sensitive robot in an inhomogeneous environment and a model of motility-induced phase separation (MIPS). We studied singular limits of these systems obtained by (nonrigorous) singular perturbation theory and found some puzzling phenomena:  the system with only one noise source converges (in law) to a system driven by two independent noises and the singular limit acquires an additional drift term which does not correspond to any term in the original equation. I will report on a general theorem which covers the applications mentioned above and much more, explaining the structure of the limiting equations. The work has been done jointly with Tanner Reese as a part of his RTG project. The paper containing the results has been submitted to arXiv.

(https://arizona.zoom.us/j/87802949465)