Related papers: Lectures on two-dimensional critical percolation
These notes fill in results about oriented percolation that are required for the paper [3] ("Forward clusters for degenerate random environments"). Since these are essentially modifications of results found in other sources (but adapted to…
These are expanded lecture notes for the summer school on Berkovich spaces that took place at the Institut de Math\'ematiques de Jussieu, Paris in 2010. They serve to illustrate some techniques and results from the dynamics on…
Closing talk at Snowmass 2001: a summer study on the future of particle physics.
We study invasion percolation in two dimensions. We compare connectivity properties of the origin's invaded region to those of (a) the critical percolation cluster of the origin and (b) the incipient infinite cluster. To exhibit…
This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.
These are the notes from a course of five lectures at the 2009 Park City Math Institute. The focus is on elliptic curves over function fields over finite fields. In the first three lectures, we explain the main classical results (mainly due…
One of the most well-known classical results for site percolation on the square lattice is the equation $p_c+p_c^*=1$. In words, this equation means that for all values $\neq p_c$ of the parameter $p$, the following holds: either a.s. there…
These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.
Extra dimensions provide a new window on a number of problems faced by the Standard Model. The following provides an introduction to this very broad subject aimed at experimental graduate students and post-docs based on a lecture given at…
The percolation study offers valuable insights into the characteristics of phase transition, shedding light on the underlying mechanisms that govern the formation of global connectivity within the system. We explore the percolation phase…
We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
Lecture notes from a minicourse given at the ICTP in May 2002.
The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal…
We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.
We give a self-contained and detailed presentation of Kesten's results that allow to relate critical and near-critical percolation on the triangular lattice. They constitute an important step in the derivation of the exponents describing…
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
I review some of the results presented in the working group on diffraction at DIS97, with a particular emphasis on the theory of diffractive hard scattering.
These lecture notes consist of two major connected parts. The first part (Sections 1, 2), after a brief historical introduction, deals with the physics of critical points in thermodynamic equilibrium. The features of the fluctuations…
This is a short survey of work on percolation and first-passage percolation since the publication (in 1996 and 1984, respectively) of the two authors' Saint-Flour notes on these topics.