کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1843019 | 1031501 | 2011 | 32 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
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چکیده انگلیسی
We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nuclear Physics B - Volume 848, Issue 2, 11 July 2011, Pages 398-429
Journal: Nuclear Physics B - Volume 848, Issue 2, 11 July 2011, Pages 398-429
نویسندگان
Gabriel Álvarez, Luis MartÃnez Alonso, Elena Medina,