Winding of Planar Stationary Gaussian Processes

Tuesday, March 24, 2015 - 2:00pm - 3:00pm
Lind 305
Naomi Feldheim (University of Minnesota, Twin Cities)
Consider the path of a shift-invariant random map from the real numbers to the complex plane whose finite marginal distributions are Gaussian. Such processes are used by physicists to model polymers and random flux lines of magnetic fields. We investigate the winding number of such paths around the origin. We give exact forumlae for the mean and variance of this quantity, and prove a Central limit theorem. In doing so, we give rigorous proofs to predictions by physicists, such as Le Doussal, Etzioni and Horovitz.