1,566 research outputs found
Brane Tensions and Coupling Constants from within M-Theory
Reviewing the cancellation of local anomalies of M-theory on R^10 x S^1/Z_2
the Yang-Mills coupling constant on the boundaries is rederived. The result is
lambda^2 = 2^(1/3) (2 pi) (4 pi kappa^2)^(2/3) corresponding to eta =
lambda^6/kappa^4 = 256 pi^5 in the `upstairs' units used by Horava and Witten
and differs from their calculation. It is shown that these values are
compatible with the standard membrane and fivebrane tensions derived from the
M-theory bulk action. In view of these results it is argued that the natural
units for M-theory on R^10 x S^1/Z_2 are the `downstairs' units where the brane
tensions take their standard form and the Yang-Mills coupling constant is
lambda^2 = 4 pi (4 pi kappa^2)^(2/3).Comment: 11 pages, no figures, Latex2e, amsmath, amsfonts, typo in abstract
correcte
Weak Convergence in the Prokhorov Metric of Methods for Stochastic Differential Equations
We consider the weak convergence of numerical methods for stochastic
differential equations (SDEs). Weak convergence is usually expressed in terms
of the convergence of expected values of test functions of the trajectories.
Here we present an alternative formulation of weak convergence in terms of the
well-known Prokhorov metric on spaces of random variables. For a general class
of methods, we establish bounds on the rates of convergence in terms of the
Prokhorov metric. In doing so, we revisit the original proofs of weak
convergence and show explicitly how the bounds on the error depend on the
smoothness of the test functions. As an application of our result, we use the
Strassen - Dudley theorem to show that the numerical approximation and the true
solution to the system of SDEs can be re-embedded in a probability space in
such a way that the method converges there in a strong sense. One corollary of
this last result is that the method converges in the Wasserstein distance,
another metric on spaces of random variables. Another corollary establishes
rates of convergence for expected values of test functions assuming only local
Lipschitz continuity. We conclude with a review of the existing results for
pathwise convergence of weakly converging methods and the corresponding strong
results available under re-embedding.Comment: 12 pages, 2nd revision for IMA J Numerical Analysis. Further minor
errors correcte
Some cubic birth and death processes and their related orthogonal polynomials
The orthogonal polynomials with recurrence relation (\la\_n+\mu\_n-z)
F\_n(z)=\mu\_{n+1} F\_{n+1}(z)+\la\_{n-1} F\_{n-1}(z) with two kinds of cubic
transition rates \la\_n and corresponding to indeterminate
Stieltjes moment problems, are analyzed. We derive generating functions for
these two classes of polynomials, which enable us to compute their Nevanlinna
matrices. We discuss the asymptotics of the Nevanlinna matrices in the complex
plane.Comment: latex2e, 17 page
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