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UNITARY MATRIX INTEGRALS
, 2006
"... Abstract. We prove that the limit of various unitary matrix integrals, including the ItzyksonZuber integral, exists in a small parameters region and is analytic in these parameters. ..."
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Cited by 2 (1 self)
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Abstract. We prove that the limit of various unitary matrix integrals, including the ItzyksonZuber integral, exists in a small parameters region and is analytic in these parameters.
On the digraph of a unitary matrix
 SIAM Journal of Matrix Analysis and Applications
, 2003
"... Abstract. Given a matrix M of size n, the digraph D on n vertices is said to be the digraph of M, when Mij ̸ = 0 if and only if (vi, vj) is an arc of D. We give a necessary condition, called strong quadrangularity, for a digraph to be the digraph of a unitary matrix. With the use of such a condition ..."
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Cited by 27 (10 self)
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Abstract. Given a matrix M of size n, the digraph D on n vertices is said to be the digraph of M, when Mij ̸ = 0 if and only if (vi, vj) is an arc of D. We give a necessary condition, called strong quadrangularity, for a digraph to be the digraph of a unitary matrix. With the use of such a
ON THE PATTERN OF A UNITARY MATRIX
, 2002
"... Abstract. Given a digraph D on n vertices, a matrix A of size n is said to have pattern D, if it has entry Aij ̸ = 0 if and only if (vi, vj) is an arc of D. We give a necessary condition, which is called strong quadrangularity, for a digraph to be the pattern of a unitary matrix. With the use of suc ..."
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Cited by 1 (0 self)
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Abstract. Given a digraph D on n vertices, a matrix A of size n is said to have pattern D, if it has entry Aij ̸ = 0 if and only if (vi, vj) is an arc of D. We give a necessary condition, which is called strong quadrangularity, for a digraph to be the pattern of a unitary matrix. With the use
ASYMPTOTICS OF UNITARY MATRIX INTEGRALS
, 2007
"... In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large N limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and investigate examples related to free probability and the HCIZ i ..."
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Cited by 1 (0 self)
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In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large N limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and investigate examples related to free probability and the HCIZ
Defect of a unitary matrix
, 2007
"... We analyze properties of a map B = f(U) sending a unitary matrix U of size N into a doubly stochastic matrix defined by Bi,j = Ui,j  2. For any U we define its defect, determined by the dimensionality of the space being the image Df (TUU) of the space TUU tangent to the manifold of unitary matrice ..."
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Cited by 8 (0 self)
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We analyze properties of a map B = f(U) sending a unitary matrix U of size N into a doubly stochastic matrix defined by Bi,j = Ui,j  2. For any U we define its defect, determined by the dimensionality of the space being the image Df (TUU) of the space TUU tangent to the manifold of unitary
Bulk Universality for Unitary Matrix Models
, 804
"... We give a proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally C 2 and locally C 3 function (see Theorem 1.2). The proof is based on the determinant formulas for correlation functions in terms of polynomials orthogonal on the unit circle. We ..."
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We give a proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally C 2 and locally C 3 function (see Theorem 1.2). The proof is based on the determinant formulas for correlation functions in terms of polynomials orthogonal on the unit circle
Unitary matrix model for toroidal compactifications
 of M theory,” Phys. Lett. B
, 1997
"... A unitary matrix model is proposed as the largeN matrix formulation of M theory on flat space with toroidal topology. The model reproduces the motion of elementary Dparticles on the compact space, and admits membrane states with nonzero wrapping around nontrivial 2tori even at finite N. ..."
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Cited by 2 (0 self)
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A unitary matrix model is proposed as the largeN matrix formulation of M theory on flat space with toroidal topology. The model reproduces the motion of elementary Dparticles on the compact space, and admits membrane states with nonzero wrapping around nontrivial 2tori even at finite N.
Unitary matrix models and Painlevé III
 Mod. Phys. Letts A11
, 1996
"... We discussed the full unitary matrix models from the view points of integrable equations and string equations. Coupling the Toda equations and the string equations, we derive a special case of the Painlevé III equation. From the Virasoro constrains, we can use the radial coordinate. The relation bet ..."
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We discussed the full unitary matrix models from the view points of integrable equations and string equations. Coupling the Toda equations and the string equations, we derive a special case of the Painlevé III equation. From the Virasoro constrains, we can use the radial coordinate. The relation
Unitary Matrix Models and Phase Transition
, 2008
"... We study the unitary matrix model with a topological term. We call the topological term the theta term. In the symmetric model there is the phase transition at λc = 2. If the Wilson term is larger than the theta term, there is the phase transition at the same λc. On the other hand, if the theta term ..."
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We study the unitary matrix model with a topological term. We call the topological term the theta term. In the symmetric model there is the phase transition at λc = 2. If the Wilson term is larger than the theta term, there is the phase transition at the same λc. On the other hand, if the theta
Results 1  10
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1,825