By Gregory F. Lawler

Theoretical physicists have anticipated that the scaling limits of many two-dimensional lattice versions in statistical physics are in a few feel conformally invariant. This trust has allowed physicists to foretell many amounts for those severe platforms. the character of those scaling limits has lately been defined accurately by utilizing one recognized software, Brownian movement, and a brand new development, the Schramm-Loewner evolution (SLE). This publication is an creation to the conformally invariant tactics that seem as scaling limits. the next themes are lined: stochastic integration; advanced Brownian movement and measures derived from Brownian movement; conformal mappings and univalent features; the Loewner differential equation and Loewner chains; the Schramm-Loewner evolution (SLE), that's a Loewner chain with a Brownian movement enter; and purposes to intersection exponents for Brownian movement. the must haves are first-year graduate classes in actual research, complicated research, and likelihood. The publication is appropriate for graduate scholars and examine mathematicians attracted to random methods and their purposes in theoretical physics.