排序方式: 共有26条查询结果,搜索用时 31 毫秒
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We study random skew 3D partitions weighted by q
vol
and, specifically, the q → 1 asymptotics of local correlations near various points of the limit shape. We obtain sine-kernel asymptotics for correlations in the bulk of the disordered region, Airy kernel asymptotics near a general point of the frozen boundary, and a Pearcey kernel asymptotics near a cusp of the frozen boundary. 相似文献
3.
A. Yu. Okounkov 《Functional Analysis and Its Applications》2002,36(2):134-139
We concisely and directly prove that the interpolation Macdonald polynomials are orthogonal with respect to the Fourier pairing and briefly discuss immediate applications of this fact, in particular, to the symmetry of the Fourier pairing and to the binomial formula. 相似文献
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We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm, Mariño, and Vafa of the Gromov-Witten theory of local Calabi-Yau toric 3-folds are proven to be correct in the full 3-leg setting. 相似文献
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We prove a formula expressing a generaln byn Toeplitz determinant as a Fredholm determinant of an operator 1 –K acting onl
2
(n,n+1,...), where the kernelK admits an integral representation in terms of the symbol of the original Toeplitz matrix. The proof is based on the results of one of the authors, see [14], and a formula due to Gessel which expands any Toeplitz determinant into a series of Schur functions. We also consider 3 examples where the kernel involves the Gauss hypergeometric function and its degenerations. 相似文献
7.
We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points of ℂ2. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum Calogero-Sutherland
many-body system. A relationship between the quantum cohomology of the Hilbert scheme and the Gromov-Witten/Donaldson-Thomas
correspondence for local curves is proven. 相似文献
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In this paper we study surfaces in R
3 that arise as limit shapes in random surface models related to planar dimers. These limit shapes are surface tension minimizers, that is, they minimize a functional of the form ∫σ(∇h) dx
dy among all Lipschitz functions h taking given values on the boundary of the domain. The surface tension σ has singularities and is not strictly convex, which leads to formation of facets and edges in the limit shapes.
We find a change of variables that reduces the Euler–Lagrange equation for the variational problem to the complex inviscid
Burgers equation (complex Hopf equation). The equation can thus be solved in terms of an arbitrary holomorphic function, which
is somewhat similar in spirit to Weierstrass parametrization of minimal surfaces. We further show that for a natural dense
set of boundary conditions, the holomorphic function in question is, in fact, algebraic. The tools of algebraic geometry can thus be brought in to study the minimizers and, especially, the formation of their singularities.
This is illustrated by several explicitly computed examples. 相似文献
10.
A. Okounkov 《Selecta Mathematica, New Series》2001,7(1):57-81
We use representation theory to obtain a number of exact results for random partitions. In particular, we prove a simple determinantal formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching generalization of the Plancherel measure; see [3], [8]) and also observe that these correlations functions are t \tau -functions for the Toda lattice hierarchy. We also give a new proof of the formula due to Bloch and the author [5] for the so-called n-point functions of the uniform measure on partitions and comment on the local structure of a typical partition. 相似文献