95,801 research outputs found
Bulk asymptotics of skew-orthogonal polynomials for quartic double well potential and universality in the matrix model
We derive bulk asymptotics of skew-orthogonal polynomials (sop)
\pi^{\bt}_{m}, , 4, defined w.r.t. the weight , , and . We assume that as there
exists an , such that , where is the critical value which separates
sop with two cuts from those with one cut. Simultaneously we derive asymptotics
for the recursive coefficients of skew-orthogonal polynomials. The proof is
based on obtaining a finite term recursion relation between sop and orthogonal
polynomials (op) and using asymptotic results of op derived in \cite{bleher}.
Finally, we apply these asymptotic results of sop and their recursion
coefficients in the generalized Christoffel-Darboux formula (GCD) \cite{ghosh3}
to obtain level densities and sine-kernels in the bulk of the spectrum for
orthogonal and symplectic ensembles of random matrices.Comment: 6 page
Matrices coupled in a chain. I. Eigenvalue correlations
The general correlation function for the eigenvalues of complex hermitian
matrices coupled in a chain is given as a single determinant. For this we use a
slight generalization of a theorem of Dyson.Comment: ftex eynmeh.tex, 2 files, 8 pages Submitted to: J. Phys.
2048 is (PSPACE) Hard, but Sometimes Easy
We prove that a variant of 2048, a popular online puzzle game, is
PSPACE-Complete. Our hardness result holds for a version of the problem where
the player has oracle access to the computer player's moves. Specifically, we
show that for an game board , computing a sequence of
moves to reach a particular configuration from an initial
configuration is PSPACE-Complete. Our reduction is from
Nondeterministic Constraint Logic (NCL). We also show that determining whether
or not there exists a fixed sequence of moves of length that results in a
winning configuration for an game board is fixed-parameter
tractable (FPT). We describe an algorithm to solve this problem in
time.Comment: 13 pages, 11 figure
Assessing Microfinance for Water and Sanitation: Exploring Opportunities for Sustainable Scaling Up
The objective of this study, commissioned by the Bill & Melinda Gates Foundation, is to assess the potential market for using microfinance in the water and sanitation sector, and to identify specific opportunities for potential learning, investment, and support. This report focuses on these opportunities and suggests measures that are needed for sustainable scaling up, which can be supported by the Bill & Melinda Gates Foundation and other development institutions
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