21,835 research outputs found
Viscosity methods giving uniqueness for martingale problems
Let be a complete, separable metric space and be an operator on
. We give an abstract definition of viscosity sub/supersolution of the
resolvent equation and show that, if the comparison principle
holds, then the martingale problem for has a unique solution. Our proofs
work also under two alternative definitions of viscosity sub/supersolution
which might be useful, in particular, in infinite dimensional spaces, for
instance to study measure-valued processes.
We prove the analogous result for stochastic processes that must satisfy
boundary conditions, modeled as solutions of constrained martingale problems.
In the case of reflecting diffusions in , our assumptions
allow to be nonsmooth and the direction of reflection to be degenerate.
Two examples are presented: A diffusion with degenerate oblique direction of
reflection and a class of jump diffusion processes with infinite variation jump
component and possibly degenerate diffusion matrix
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Repetition-free longest common subsequence of random sequences
A repetition free Longest Common Subsequence (LCS) of two sequences x and y
is an LCS of x and y where each symbol may appear at most once. Let R denote
the length of a repetition free LCS of two sequences of n symbols each one
chosen randomly, uniformly, and independently over a k-ary alphabet. We study
the asymptotic, in n and k, behavior of R and establish that there are three
distinct regimes, depending on the relative speed of growth of n and k. For
each regime we establish the limiting behavior of R. In fact, we do more, since
we actually establish tail bounds for large deviations of R from its limiting
behavior.
Our study is motivated by the so called exemplar model proposed by Sankoff
(1999) and the related similarity measure introduced by Adi et al. (2007). A
natural question that arises in this context, which as we show is related to
long standing open problems in the area of probabilistic combinatorics, is to
understand the asymptotic, in n and k, behavior of parameter R.Comment: 15 pages, 1 figur
Masses of the Goldstone modes in the CFL phase of QCD at finite density
We construct the U_L(3) x U_R(3) effective lagrangian which encodes the
dynamics of the low energy pseudoscalar excitations in the Color-Flavor-Locking
superconducting phase of QCD at finite quark density. We include the effects of
instanton-induced interactions and study the mass pattern of the pseudoscalar
mesons. A tentative comparison with the analytical estimate for the gap
suggests that some of these low energy momentum modes are not stable for
moderate values of the quark chemical potential.Comment: 15 pages, 5 figures; Discussion of quark mass effects at very large
densities amended, references adde
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