Related papers: Lectures on two-dimensional critical percolation
This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.
We argue that clustering of color sources, leading to the percolation transition, may be the way to achieve deconfinement in heavy ion collisions. The critical density for percolation is related to the effective critical temperature of the…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.
This is a write-up of two lectures on AdS/CFT correspondance given by the authors at the 1998 Spring School at the Abdus Salam ICTP
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.
We consider independent and $m$-dependent two-dimensional oriented site percolation with open-site density close to one started from Bernoulli product measures. We show that the probability of an occupied interval in the former process…
This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy.
Some considerations are reported, freely inspired from the presentations and discussions during the Beijing Normal University Workshop on the above Subject, held in July 2007. Of course this cannot be a complete summary but just a…
In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing…
This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…
The present notes contain the material of the lectures given by the author at the summer school on ``Modular Forms and their Applications'' at the Sophus Lie Conference Center in the summer of 2004.
Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. We introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and…
Lectures presented at the Les Houches 2016 Summer School "Integrability: from Statistical Systems to Gauge Theory".
We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at/near critical external fields. We show that all scaling relations, except a single hyperscaling relation, hold under the power…
Lectures presented at the 42nd Scottish Universities Summer School in Physics, St. Andrews, Scotland, August 1993.
The nature of level set percolation in the two-dimension Gaussian Free Field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition, and characterize the critical point. In…
The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its continuity or discontinuity depending on the cluster weight…
These are the lecture notes from a course given in July 2005 at the summer school in Les Houches. We describe some recent results concerning two-dimensional conformally invariant systems. In particular, we discuss conformally invariant…
Lectures note for Cargese 99 Summer School Particle Physics: Ideas and Recent Development NATO Advanced Institute, Corsica, July 26-August 7, 1999
Lectures given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009