相关论文: Lectures on two-dimensional critical percolation

Information percolation is a new method for analyzing stochastic spin systems through classifying and controlling the clusters of information-flow in the space-time slab. It yielded sharp mixing estimates (cutoff with an $O(1)$-window) for…

Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…

Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…

In four lectures, delivered at the TASI 2010 summer school, I cover selected topics in the application of the gauge-string duality to nuclear and condensed matter physics. On the nuclear side, I focus on multiplicity estimates from trapped…

We study the RHIC data on long range rapidity correlations, comparing their main trends with different string model simulations. Particular attention is paid to color percolation model and its similarities with color glass condensate. As…

This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).

We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…

These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.

Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two…

These are notes for an advanced course given at Ben Gurion University in Spring 2012.

Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour…

The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…

This is the preliminary version of a book on Coulomb and Riesz gases that grew out of a set of notes written for graduate courses taught at the Courant Institute, at the Ecole Normale Sup\'erieure, and at the 2024 Saint-Flour Probability…

These are lecture notes on causal set theory prepared in Jan. 2002 for a Summer School in Valdivia, Chile. In some places, they are more complete, in others much less so, regrettably. An extensive set of references and a glossary of terms…

The relativistic heavy ion collider (RHIC) offers many opportunities to study diffraction in pp, pA and AA collisions. Because both proton beams can be polarized, RHIC offers the unique possibility of studying polarization effects in…

A simple non-interacting-electron model, combining local quantum tunneling and global classical percolation (due to a finite dephasing time at low temperatures), is introduced to describe a metal-insulator transition in two dimensions. It…

I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase…

We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…

This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…

This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.