Approximate counting, phase transitions and geometry of polynomials

Jingcheng Liu

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2019-110
August 1, 2019

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2019/EECS-2019-110.pdf

In classical statistical physics, a phase transition is understood by studying the geometry (the zero-set) of an associated polynomial (the partition function). In this thesis, we will show that one can exploit this notion of phase transitions algorithmically, and conversely exploit the analysis of algorithms to understand phase transitions.

As applications, we give efficient deterministic approximation algorithms (FPTAS) for counting q-colorings, and for computing the partition function of the Ising model.

Advisor: Alistair Sinclair


BibTeX citation:

@phdthesis{Liu:EECS-2019-110,
    Author = {Liu, Jingcheng},
    Title = {Approximate counting, phase transitions and geometry of polynomials},
    School = {EECS Department, University of California, Berkeley},
    Year = {2019},
    Month = {Aug},
    URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2019/EECS-2019-110.html},
    Number = {UCB/EECS-2019-110},
    Abstract = {In classical statistical physics, a phase transition is understood by studying the geometry (the zero-set) of an associated polynomial (the partition function).  In this thesis, we will show that one can exploit this notion of phase transitions algorithmically, and conversely exploit the analysis of algorithms to understand phase transitions.  

As applications, we give efficient deterministic approximation algorithms (FPTAS) for counting q-colorings, and for computing the partition function of the Ising model.}
}

EndNote citation:

%0 Thesis
%A Liu, Jingcheng
%T Approximate counting, phase transitions and geometry of polynomials
%I EECS Department, University of California, Berkeley
%D 2019
%8 August 1
%@ UCB/EECS-2019-110
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2019/EECS-2019-110.html
%F Liu:EECS-2019-110