Dear colleagues, On June Thursday 24 at 15:30, dr. Elena Magnanini (Università degli Studi di Padova) will give a virtual seminar “in Florence”, to which you are all invited. You can find title and abstract below. Title: Limit theorems for exponential random graphs Abstract: In the present talk we focus on the derivation of some asymptotic properties for the family of exponential random graphs. This model can be seen as the generalization of the dense Erdӧs-Rényi random graph and follows the statistical mechanics approach of defining a Hamiltonian to weight the probability measure on the space of graphs, assigning higher mass to graphs with “desirable” properties. In particular our analysis will be focused on the edge-triangle model, a two-parameter family of exponential random graphs where the Hamiltonian only includes edge and triangle densities. We borrow tools from statistical mechanics together with large deviations techniques to obtain limit theorems for the edge density in the so-called replica symmetric regime, where the limiting free energy of the model is known together with a complete characterization of the phase diagram. First, we determine the asymptotic distribution of the edge density, as the graph size n tends to infinity, in the entire replica symmetric regime. We then study the fluctuations of the edge density around its average for all parameter values outside the critical curve and off the critical point and we formulate conjectures about the behavior at criticality based on the analysis of a mean-field approximation of the model. Some of our results can be extended with no substantial changes to more general classes of exponential random graphs. Joint work with Alessandra Bianchi and Francesca Collet. The seminar will be on Zoom. You can find the information to join below. Time: Jun 24, 2021 03:30 PM Rome Join Zoom Meeting https://us02web.zoom.us/j/86107880384?pwd=UllNZWhmM1FZclB1TnF0U2p1QVZtUT09 Meeting ID: 861 0788 0384 Passcode: 149060 If you know of someone who might be interested and is not subscribed to the random mailing list, please do not hesitate to forward this announcement to them. Kind regards, Gianmarco ---------------------------------------------------------------------- Gianmarco Bet (he/him) Junior researcher https://gianmarco.bet Phone: (+39) 055 2751491 Department of Mathematics and Informatics "U. Dini" University of Florence Viale Morgagni, 65 50134 Firenze, Italy Office 64 ----------------------------------------------------------------------