Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Nicholas M. Ercolani"'
Publikováno v:
Mathematical Physics, Analysis and Geometry. 26
We study extensions of the classical Toda lattices at several different space-time scales. These extensions are from the classical tridiagonal phase spaces to the phase space of full Hessenberg matrices, referred to as the Full Kostant-Toda Lattice.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ba43d304a2d75e601730024c0956a7e
https://doi.org/10.1007/s11040-022-09444-3
https://doi.org/10.1007/s11040-022-09444-3
Publikováno v:
Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 37:79-103
We study the Ginzburg-Landau equations on Riemann surfaces of arbitrary genus. In particular: - we construct explicitly the (local moduli space of gauge-equivalent) solutions in a neighbourhood of the constant curvature ones; - classify holomorphic s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b2bdbd0fb8722f1f7f7d25ef4fdb01ca
https://doi.org/10.1016/j.anihpc.2019.04.002
https://doi.org/10.1016/j.anihpc.2019.04.002
Autor:
Nicholas M. Ercolani, Patrick Waters
Publikováno v:
Random Matrices: Theory and Applications. 11
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of construction
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f53076872c3edb85896d7047d963947
https://doi.org/10.1142/s201032632250037x
https://doi.org/10.1142/s201032632250037x
In this paper, we introduce the ghost-box-ball system, which is an extended version of the classical soliton cellular automaton. It is initially motivated as a mechanism for making precise a connection between the Schensted insertion (of the Robinson
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::18d7eb27cf143f8ed9ceba356ab1c156
http://arxiv.org/abs/2101.07896
http://arxiv.org/abs/2101.07896
Publikováno v:
Journal of Theoretical Probability. 32:1-46
We propose a novel complex-analytic method for sums of i.i.d. random variables that are heavy-tailed and integer-valued. The method combines singularity analysis, Lindel\"of integrals, and bivariate saddle points. As an application, we prove three th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fdc0a6acb6f2b6dd13438fe955b17908
https://doi.org/10.1007/s10959-018-0832-2
https://doi.org/10.1007/s10959-018-0832-2
Publikováno v:
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. 376(2117)
This article discusses numerical and analytical results on grain boundaries, which are line defects that separate roll patterns oriented in different directions. The work is set in the context of a canonical pattern-forming system, the Swift–Hohenb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dce76f6502ab078b563dda25d0ad3968
https://pubmed.ncbi.nlm.nih.gov/29507177
https://pubmed.ncbi.nlm.nih.gov/29507177
Autor:
Nicholas M. Ercolani
Publikováno v:
Nonlinearity. 24:481-526
This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::33da0ede3c6880854954e8d1fdab89d4
https://doi.org/10.1088/0951-7715/24/2/006
https://doi.org/10.1088/0951-7715/24/2/006
Publikováno v:
Communications on Pure and Applied Mathematics. 48:1369-1440
Generic wave train solutions to the complex Ablowitz-Ladik equations are developed using methods of algebraic geometry. The inverse spectral transform is used to realize these solutions as potentials in a spatially discrete linear operator. The manif
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eb60e2b1791bfefddecea38b860e307a
https://doi.org/10.1002/cpa.3160481203
https://doi.org/10.1002/cpa.3160481203
Publikováno v:
Communications in Mathematical Physics. 278:31-81
In this paper we derive a hierarchy of differential equations which uniquely determine the coefficients in the asymptotic expansion, for large $N$, of the logarithm of the partition function of $N \times N$ Hermitian random matrices. These coefficien
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::779c9d7022b3c0c1fe1112bb341c93a7
https://doi.org/10.1007/s00220-007-0395-z
https://doi.org/10.1007/s00220-007-0395-z