Elnur Emrah (KTH)
Speaker: Elnur Emrah (KTH)
Title: Exit point bounds in exponential last-passage percolation and a few applications
Abstract: One versatile probabilistic approach to study directed percolation and polymer models is through comparison with their equilibrium versions when the latter are sufficiently tractable and provide a satisfactory approximation for the purposes of the problem at hand. In this talk, we focus on the paradigmatic setting of last-passage percolation with i.i.d. exponential weights on the lattice quadrant. The equilibrium versions of this model are explicitly obtained byplacing additional independent exponential weights with suitable rates on the boundary (axes). Then an important aspect of the aforementioned comparison scheme is to control the point where a given geodesic from the origin exits the boundary. The main resultsto be presented in the talk are sharp upper bounds on the tails of the exit points. While these bounds can be and, in part, have been concurrently established via known tail bounds for the largest eigenvalue of the Laguerre ensemble, our technique is new andrelies entirely on the stationarity of the equilibrium models. We also aim to discuss two applications of the exit bounds related to the geometry of geodesics. These results provide upper bounds on the speed of distributional convergence to the Busemann limitsand to the limiting direction of the competition interface.
Joint work with C. Janjigian and T. Sepp盲l盲inen.
Link:
Meeting ID: 970 9325 9428
Passcode: problab
听
听