ARC Colloquium: Andreas Galanis - University of Oxford

Event Details
  • Date/Time:
    • Wednesday August 26, 2015 - Thursday August 27, 2015
      2:05 pm - 2:59 pm
  • Location: Klaus Classroom 2447
  • Phone:
  • URL: http://www.arc.gatech.edu/
  • Email:
  • Fee(s):
    N/A
  • Extras:
Contact

Dani Denton

denton at cc dot gatech dot edu

Summaries

Summary Sentence: Klaus 2447 at 4 pm (Note: time and location are different than usual)

Full Summary: No summary paragraph submitted.

Algorithms & Randomness Center (ARC) Colloquium

Andreas Galanis – University of Oxford

Wednesday, August 26, 2015

Klaus 2447 - 2:00 pm

 Title:

Swendsen-Wang Algorithm on the Mean-Field Potts Model

Abstract:

This talk will focus on the q-state ferromagnetic Potts model on the n-vertex complete graph known as the mean-field (Curie-Weiss) model. We analyze the Swendsen-Wang algorithm which is a Markov chain that utilizes the random cluster representation for the ferromagnetic Potts model to recolor large sets of vertices in one step and potentially overcomes obstacles that inhibit single-site Glauber dynamics. 

 The case q=2 (the Swendsen-Wang algorithm for the ferromagnetic Ising model) undergoes a slow-down at a critical temperature beta=betac (Long et al., 2014), but yet still has polynomial mixing time at all (inverse) temperatures beta>0 (Cooper et al., 2000). 

 In contrast, for q>=3 there are two critical temperatures 0<betau<betarc that are relevant (these correspond to phase transitions on the infinite tree). We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: 

(i) O(log n) for beta<betau, (ii) O(n^{1/3}) for beta=betau, (iii) exp(n^(Omega(1))) for betau<beta<betarc, and (iv) O(log n) for beta>=betarc. These results complement refined results of Cuff et al. (2012) on the mixing time of the Glauber dynamics for the ferromagnetic Potts model.

 The most interesting aspect of our analysis is at the critical temperature beta=betau, which requires a delicate choice of a potential function to balance the conflating factors for the slow drift away from a fixed point (which is repulsive but not Jacobian repulsive): close to the fixed point the variance from the percolation step dominates and sufficiently far from the fixed point the dynamics of the size of the dominant color class takes over.

Joint work with Daniel Stefankovic and Eric Vigoda.

Additional Information

In Campus Calendar
No
Groups

College of Computing, School of Computer Science, ARC

Invited Audience
Undergraduate students, Faculty/Staff, Public, Graduate students
Categories
Seminar/Lecture/Colloquium
Keywords
(ARC), Algorithm and Randomness Center, Computational Complexity, Computational Learning Theory, Georgia Tech, Swendsen-Wang algorithm
Status
  • Created By: Dani Denton
  • Workflow Status: Published
  • Created On: Aug 18, 2015 - 9:42am
  • Last Updated: Apr 13, 2017 - 5:18pm