Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore advanced asymptotic enumeration techniques for regular graphs in this 57-minute lecture from the IAS/PCMI Park City Mathematics Institute. Delve into the third part of a comprehensive series examining three primary methods for counting regular graphs: the configuration model and switchings, generating functions combined with saddle point methods, and the relatively recent Stein's method approach utilizing degree switchings to derive recursive formulas. Focus particularly on the Stein's method while understanding how these enumeration techniques extend beyond mere counting to applications in generating graphs with specified degree sequences, network design and testing, network dynamics analysis, and real-world system modeling. Build upon basic discrete probability theory foundations while leveraging knowledge of concentration inequalities such as Chernoff and Azuma-Hoeffding bounds, though no prior experience with graph enumeration by degree sequence is required. Access accompanying lecture notes and problem sets to reinforce the mathematical concepts presented in this graduate-level exploration of probabilistic and extremal combinatorics.
