Igor Kortchemski (Ecole Polytechnique)
CRM-ISM Probability Seminar
Title: Biconditioned Planar Maps
Abstract: Consider all soccer balls having n^a edges obtained by gluing n polygons, and take one uniformly at random; what does it look like when n is large? More formally, what is the structure of random planar maps sampled at random according to face degree weights and which are conditioned at the same time by their number of vertices, edges and faces? We will see in particular that typical distances in uniform maps with n^a edges and n faces is n^((2a-1)/4), which confirms a prediction of Fusy & Guitter. Thanks to known bijections, we will see that this amounts to establishing scaling limits of nondecreasing integer-valued random walks conditioned by their terminal value at time n in various regimes, which is of independent interest. Joint work with Cyril Marzouk.
Link:
Meeting ID: 875 9669 4672
Passcode: problab