Fonctionne avec Indico
v3.2.9
Consider a random walk on the d dimensional torus of size length N, d>2, and let T be the average of the first time all the vertices of the torus have been visited by this walk. For 0<α<1, the α-late points are defined as the vertices not visited by this walk at time αT. It is known that for α large enough the α-late points are essentially i.i.d. on the torus, whereas this is not the case for α small enough. I will explain why this phase transition actually happens at some parameter α*>1/2, which can be explicitly written in terms of the Green function on the d-dimensional infinite lattice. I will also describe the law of these α-late points in the non i.i.d. region 1/2<α<α*. Based on joint work with Pierre-François Rodriguez and Perla Sousi.