182,312 research outputs found
Uncertainty of flow in porous media
The problem posed to the Study Group was, in essence, how to estimate the probability distribution of f(x) from the probability distribution of x. Here x is a large vector and f is a complicated function which can be expensive to evaluate. For Schlumberger's applications f is a computer simulator of a hydrocarbon reservoir, and x is a description of the geology of the reservoir, which is uncertain
Validity of the expected Euler characteristic heuristic
We study the accuracy of the expected Euler characteristic approximation to
the distribution of the maximum of a smooth, centered, unit variance Gaussian
process f. Using a point process representation of the error, valid for
arbitrary smooth processes, we show that the error is in general exponentially
smaller than any of the terms in the approximation. We also give a lower bound
on this exponential rate of decay in terms of the maximal variance of a family
of Gaussian processes f^x, derived from the original process f.Comment: Published at http://dx.doi.org/10.1214/009117905000000099 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Localization and delocalization of random interfaces
The probabilistic study of effective interface models has been quite active
in recent years, with a particular emphasis on the effect of various external
potentials (wall, pinning potential, ...) leading to
localization/delocalization transitions. I review some of the results that have
been obtained. In particular, I discuss pinning by a local potential, entropic
repulsion and the (pre)wetting transition, both for models with continuous and
discrete heights.Comment: Published at http://dx.doi.org/10.1214/154957806000000050 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Conformal Anomaly and Critical Exponents of the XY-Ising Model
We use extensive Monte Carlo transfer matrix calculations on infinite strips
of widths up to 30 lattice spacing and a finite-size scaling analysis to
obtain critical exponents and conformal anomaly number for the
two-dimensional -Ising model. This model is expected to describe the
critical behavior of a class of systems with simultaneous and
symmetries of which the fully frustrated model is a special case. The
effective values obtained for show a significant decrease with at
different points along the line where the transition to the ordered phase takes
place in a single transition. Extrapolations based on power-law corrections
give values consistent with although larger values can not be ruled
out. Critical exponents are obtained more accurately and are consistent with
previous Monte Carlo simulations suggesting new critical behavior and with
recent calculations for the frustrated model.Comment: 33 pages, 13 latex figures, uses RevTeX 3.
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