3,023 research outputs found
Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited
We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts
model. We find that the Li-Sokal bound ()
is almost but not quite sharp. The ratio seems to diverge
either as a small power () or as a logarithm.Comment: 35 pages including 3 figures. Self-unpacking file containing the
LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 3 Postscript figures. Revised version fixes a
normalization error in \xi (with many thanks to Wolfhard Janke for finding
the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997
Interest rate models with Markov chains
Imperial Users onl
Theories, models, simulations: a computational challenge
In this talk I would like to illustrate with examples taken from Quantum
Field Theory and Biophysics how an intelligent exploitation of the
unprecedented power of today's computers could led not only to the solution of
pivotal problems in the theory of Strong Interactions, but also to the
emergence of new lines of interdisciplinary research, while at the same time
pushing the limits of modeling to the realm of living systems.Comment: 19 pages, 1 figure, conference pape
Deriving Matrix Concentration Inequalities from Kernel Couplings
This paper derives exponential tail bounds and polynomial moment inequalities
for the spectral norm deviation of a random matrix from its mean value. The
argument depends on a matrix extension of Stein's method of exchangeable pairs
for concentration of measure, as introduced by Chatterjee. Recent work of
Mackey et al. uses these techniques to analyze random matrices with additive
structure, while the enhancements in this paper cover a wider class of
matrix-valued random elements. In particular, these ideas lead to a bounded
differences inequality that applies to random matrices constructed from weakly
dependent random variables. The proofs require novel trace inequalities that
may be of independent interest.Comment: 29 page
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