3,760 research outputs found
Linearly edge-reinforced random walks
We review results on linearly edge-reinforced random walks. On finite graphs,
the process has the same distribution as a mixture of reversible Markov chains.
This has applications in Bayesian statistics and it has been used in studying
the random walk on infinite graphs. On trees, one has a representation as a
random walk in an independent random environment. We review recent results for
the random walk on ladders: recurrence, a representation as a random walk in a
random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Simple Amplitudes for \Phi^3 Feynman Ladder Graphs
Recently, we proposed a new approach for calculating Feynman graphs amplitude
using the Gaussian representation for propagators which was proven to be exact
in the limit of graphs having an infinite number of loops. Regge behavior was
also found in a completely new way and the leading Regge trajectory calculated.
Here we present symmetry arguments justifying the simple form used for the
polynomials in the Feynman parameters , where is the mean-value for these parameters, appearing in the amplitude for
the ladder graphs. (Taking mean-values is equivalent to the Gaussian
representation for propagators).Comment: 11 Plain TeX pages, 2 PostScript figures include
Three-State Complex Valued Spins Coupled to Binary Branched Polymers in Two-Dimensional Quantum Gravity
A model of complex spins (corresponding to a non-minimal model in the
language of CFT) coupled to the binary branched polymer sector of quantum
gravity is considered. We show that this leads to new behaviour.Comment: 3 pages, Latex2e, 2 eps figures, uses espcrc2 and epsf. Contribution
to LATTICE 97, to appear in the Proceeding
Branched polymers, complex spins and the freezing transition
We show that by coupling complex three-state systems to branched-polymer like
ensembles we can obtain models with gamma-string different from one half. It is
also possible to study the interpolation between dynamical and crystalline
graphs for these models; we find that only when geometry fluctuations are
completely forbidden is there a crystalline phase.Comment: 14 pages plain LateX2e, 4 eps figures included using eps
Regge behaviour and Regge trajectory for ladder graphs in scalar field theory
Using the gaussian representation for propagators (which can be proved to be
exact in the infinite number of loops limit) we are able to derive the Regge
behaviour for ladder graphs of field theory in a completely new way.
An analytic expression for the Regge trajectory is found in
terms of the mean-values of the Feynman -parameters.
is calculated in the range . The intercept
agrees with that obtained from earlier calculations using the Bethe-Salpeter
approach for \alpha (0) \gsim 0.3.Comment: 10 PlainTex pages, 2 PostScript Figures include
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