Lasse Leskelä

My research area is stochastics, the mathematical theory of random events, systems, and processes. The main focus is statistical network models and random graphs, together with random dynamical systems and stochastic processes acting on networks. The general objective is to derive fundamental mathematical laws for predicting the macroscopic behavior of large random systems and describing the accuracy of statistical learning algorithms for large network models. Such laws allow to make predictions using massive high-dimensional data sets for which classical methods of statistics and machine learning are often infeasible. Statistical network models under study include random intersection graphs, stochastic block models, and graphons. The archetypes of stochastic dynamics studied are branching processes, random walks, and first passage percolation. The formulas and methods have a wide range of applications ranging from information and social networks to biological and financial systems.