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401-5264-DRL 2 Credits DR D-MATH

Dimension Dependence of Critical Phenomena in Percolation

Lecturers & Examiners: Dr. Thomas Hutchcroft
Doctoral students of I-Math (UZH) need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-06-03 00:14:18

Abstract

Nachdiplom lecture

Content

In Bernoulli bond percolation, we delete or retain each edge of a graph independently at random with some retention parameter p and study the geometry of the connected components (clusters) of the resulting subgraph. For lattices of dimension d>1, percolation has a phase transition, with a infinite cluster emerging at a critical probability pc(d). It is believed that critical percolation at and near the critical probability exhibits rich, fractal-like geometry that is expected to be approximately independent of the choice of lattice but highly dependent on the dimension d. In particular, various qualitative distinctions are expected between the low dimensional case d<6, the high-dimensional case d>6, and the critical case d=6, but this remains poorly understood particularly in dimensions d=3,4,5,6. In this course, I will give an overview of what is known about critical percolation, focusing on the non-planar models and including a detailed treatment of recent advances in long-range and hierarchical models for which various aspects of intermediate-dimensional critical phenomena can now be understood rigorously.

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Course Components

Type Title Time & Place Hours
lecture Dimension Dependence of Critical Phenomena in Percolation
If you would like to attend the lecture, please register by 26 February. For the registration form see
  • Fri 10:15-12:00 (HG G 43)
  • 01.05 Date 10:15-12:00 (HG G 43)
2 h weekly

Offered In