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pro vyhledávání: '"Pierce, Virgil"'
Autor:
Pierce, Virgil
We explore two methods for calculating the Taylor Coefficients of the terms of the asymptotic expansion of the partition function of random matrices for specific even potentials. The first of these methods applies to the leading order term. We show t
Externí odkaz:
http://hdl.handle.net/10150/280566
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an investigation initiated and developed in a sequence of
Externí odkaz:
http://arxiv.org/abs/1106.1143
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy leve
Externí odkaz:
http://arxiv.org/abs/1011.4983
Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \cite{Baik:2005}. We consider the case when the $n\times n$ external sou
Externí odkaz:
http://arxiv.org/abs/1009.3894
Autor:
Kodama, Yuji, Pierce, Virgil U.
It is well-known that the partition function of the unitary ensembles of random matrices is given by a tau-function of the Toda lattice hierarchy and those of the orthogonal and symplectic ensembles are tau-functions of the Pfaff lattice hierarchy. I
Externí odkaz:
http://arxiv.org/abs/0811.0351
Autor:
Bryc, Wlodzimierz, Pierce, Virgil U.
Publikováno v:
Electronic Journal Probab. Vol. 14 (2009), Paper no. 17, pages 452--476
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner and Wishart
Externí odkaz:
http://arxiv.org/abs/0806.3695
Autor:
Kodama, Yuji, Pierce, Virgil U.
The Pfaff lattice is an integrable system arising from the SR-group factorization in an analogous way to how the Toda lattice arises from the QR-group factorization. In our recent paper [{\it Intern. Math. Res. Notices}, (2007) rnm120], we studied th
Externí odkaz:
http://arxiv.org/abs/0802.2288
Autor:
Pierce, Virgil U.
Bauer and Itzykson showed that associated to each labeled map embedded on an oriented Riemann surface there was a group generated by a pair of permutations. From this result an algorithm may be constructed for enumerating labeled maps, and this const
Externí odkaz:
http://arxiv.org/abs/math/0610586
Autor:
Pierce, Virgil U.1, Kypuros, Javier Angel1
Publikováno v:
Proceedings of the ASEE Annual Conference & Exposition. 2015, p1-11. 11p.
Autor:
Kodama, Yuji1 kodama@math.ohio-state.edu, Pierce, Virgil2 piercevu@utpa.edu
Publikováno v:
Communications in Mathematical Physics. Dec2009, Vol. 292 Issue 2, p529-568. 40p. 2 Diagrams.