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pro vyhledávání: '"Ercolani, Nicholas M."'
Autor:
Ercolani, Nicholas M.
In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connections. We focus attention on the case where there are exactly four suc
Externí odkaz:
http://arxiv.org/abs/2404.10196
Autor:
Ercolani, Nicholas M.
In this paper we establish the existence of canonical coordinates for generic co-adjoint orbits on triangular groups. These orbits correspond to a set of full Plancherel measure on the associated dual groups. This generalizes a well-known coordinatiz
Externí odkaz:
http://arxiv.org/abs/2301.12544
Publikováno v:
Mathematical Physics, Analysis and Geometry, 26:2 (2023)
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:
http://arxiv.org/abs/2203.15164
Publikováno v:
SIGMA 18 (2022), 063, 42 pages
In this paper, we perform a detailed analysis of the phase shift phenomenon of the classical soliton cellular automaton known as the box-ball system, ultimately resulting in a statement and proof of a formula describing this phase shift. This phenome
Externí odkaz:
http://arxiv.org/abs/2106.07129
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:
http://arxiv.org/abs/2101.07896
Publikováno v:
In Journal of Functional Analysis 15 October 2023 285(8)
Autor:
Ercolani, Nicholas M., Waters, Patrick
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:
http://arxiv.org/abs/1907.08026
Autor:
Brown, Tova, Ercolani, Nicholas M.
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random walks in rand
Externí odkaz:
http://arxiv.org/abs/1901.08174
Publikováno v:
J. Theor. Probab. 32, 1-46 (2019)
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:
http://arxiv.org/abs/1509.05199
Publikováno v:
Electron. J. Probab. 19, no. 82, 1-37 (2014)
We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and spatial permutations. These distributions are invari
Externí odkaz:
http://arxiv.org/abs/1401.1442