Dipl.-Math. Mario Ullrich

• Rapid mixing of Swendsen-Wang and single-bond dynamics in two dimensions,
  submitted, arXiv, 03/2012
• Swendsen-Wang is faster than single-bond dynamics,
  submitted, arXiv, 01/2012
• Comparison of Swendsen-Wang and heat-bath dynamics,
  to appear in Rand. Struct. Alg., arXiv, pdf, 05/2011
• Exact Sampling for the Ising Model at all Temperatures,
  to appear in Monte Carlo Methods Appl., arXiv, pdf, 12/2010

Other stuff:

• Survey:   Algorithms for the Ising model (with algorithms for the random-cluster model),
  Manuscript for a series of talks, pdf (ca. 70 pages), 10/2009-12/2009
• Matlab programs for "Algorithms for the Ising model" (ca. 11mb), 26.07.2010

Diploma thesis:

• Explizite Fehlerabschätzungen und der Vergleich von Importance-Sampling und dem Metropolis-Algorithmus, pdf, 07/2009

• Ising model   (Metropolis, heat-bath, Swendsen-Wang, Wolff, Propp-Wilson)
  • results
• Potts model
• Hard-core model   (or "independent sets", 2d and 3d)
• Self-avoiding walk
• Ball walk   (in arbitrary 2d or 3d cubes/ellipsoids)
• Hit-and-Run   (in 2d unit disk for bi- und trivariate Normal distributions)
• others   (discrete hypercube, queues)

• Mar. 2012, Oppurg, "Annual meeting GRK 1523":   Rapid mixing of Swendsen-Wang for the 2d Ising model at all temperatures, pdf
• Feb. 2012, Sydney (Australia), "10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing" (MCQMC 2012):   Tight mixing bounds at the Potts transition point for single-bond dynamics on the torus, pdf
• Sept. 2011, Jena, Meeting of GRK 1523 "Quantum and Gravitational Fields" (Jena) and DK "Hadrons in Vacuum, Nuclei and Stars" (Graz):   Duality-improved Swendsen-Wang dynamics for the Potts model
• Aug. 2011, Borovets (Bulgaria), "IMACS Seminar on Monte Carlo Methods" (MCM 2011):   Swendsen-Wang beats Heat-bath, pdf
• June 2011, Bonn, "Workshop on High-Dimensional Approximation" (HDA 2011):   Swendsen-Wang beats Heat-bath
• Dec. 2010, Oppurg, "Annual meeting GRK 1523":   Exact Sampling of Ising States at all Temperatures
• Oct.-Dec. 2009, Jena, series of talks:   Algorithms for the Ising model (and for the random-cluster model), pdf (ca. 70 pages)
• July 2009, Siegmundsburg:   Comparing three randomized algorithms for the hypercube, pdf

• Oberseminar Theoretische Numerik
• Oberseminar "Geometrie"
• Seminar of the research group of Prof. Lenz