6,824 research outputs found
SLE-type growth processes and the Yang-Lee singularity
The recently introduced SLE growth processes are based on conformal maps from
an open and simply-connected subset of the upper half-plane to the half-plane
itself. We generalize this by considering a hierarchy of stochastic evolutions
mapping open and simply-connected subsets of smaller and smaller fractions of
the upper half-plane to these fractions themselves. The evolutions are all
driven by one-dimensional Brownian motion. Ordinary SLE appears at grade one in
the hierarchy. At grade two we find a direct correspondence to conformal field
theory through the explicit construction of a level-four null vector in a
highest-weight module of the Virasoro algebra. This conformal field theory has
central charge c=-22/5 and is associated to the Yang-Lee singularity. Our
construction may thus offer a novel description of this statistical model.Comment: 12 pages, LaTeX, v2: thorough revision with corrections, v3: version
to be publishe
Factors determining exchange rates : a simple model and empirical tests
An abstract for this article is not availableEquilibrium (Economics)
Transforming fixed-length self-avoiding walks into radial SLE_8/3
We conjecture a relationship between the scaling limit of the fixed-length
ensemble of self-avoiding walks in the upper half plane and radial SLE with
kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a
curve from the fixed-length scaling limit of the SAW, weight it by a suitable
power of the distance to the endpoint of the curve and then apply the conformal
map of the half plane that takes the endpoint to i, then we get the same
probability measure on curves as radial SLE. In addition to a non-rigorous
derivation of this conjecture, we support it with Monte Carlo simulations of
the SAW. Using the conjectured relationship between the SAW and radial SLE, our
simulations give estimates for both the interior and boundary scaling
exponents. The values we obtain are within a few hundredths of a percent of the
conjectured values
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