# Probability and Statistical Physics in Two and More Dimensions

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*David Ellwood; Charles Newman; Vladas Sidoravicius; Wendelin Werner*

A co-publication of the AMS and Clay Mathematics Institute

This volume is a collection of lecture notes for six of the ten
courses given in Búzios, Brazil by prominent probabilists at the 2010
Clay Mathematics Institute Summer School, “Probability and Statistical
Physics in Two and More Dimensions” and at the XIV Brazilian School of
Probability.

In the past ten to fifteen years, various areas of probability
theory related to statistical physics, disordered systems and
combinatorics have undergone intensive development. A number of these
developments deal with two-dimensional random structures at their
critical points, and provide new tools and ways of coping with at
least some of the limitations of Conformal Field Theory that had been
so successfully developed in the theoretical physics community to
understand phase transitions of two-dimensional systems.

Included in this selection are detailed accounts of all three
foundational courses presented at the Clay school—Schramm–Loewner
Evolution and other Conformally Invariant Objects, Noise Sensitivity
and Percolation, Scaling Limits of Random Trees and Planar
Maps—together with contributions on Fractal and Multifractal properties of
SLE and Conformal Invariance of Lattice Models. Finally, the volume
concludes with extended articles based on the courses on Random
Polymers and Self-Avoiding Walks given at the Brazilian School of
Probability during the final week of the school.

Together, these notes provide a panoramic, state-of-the-art view of
probability theory areas related to statistical physics, disordered
systems and combinatorics. Like the lectures themselves, they are
oriented towards advanced students and postdocs, but experts should
also find much of interest.

Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

#### Readership

Graduate students and research mathematicians interested in probability and statistical physics.