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A Test of the Universality Conjecture
, 1995
"... Gammax \Gamma (n+1) in the coordinate plane. When n is large, the Aztec diamond exhibits strikingly nonhomogeneous behavior. Its boundary takes the shape of a square. The region between the boundary of the diamond and its inscribed circle is absolutely regularin each of the four connected areas at ..."
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at the corners, all the dominoes are aligned in the same direction. Within the circle, one sees a smooth transition between the four corner behaviors. See Figure 1. We call an Aztec diamond of order n an idealized Aztec diamond in the limit as n grows large. The Universality Conjecture The Universality
Lectures on Etale Cohomology
, 2008
"... These are the notes for a course taught at the University of Michigan in 1989 and 1998. In comparison with my book, the emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes. The notes also discuss the proof of the Weil conjectures (Grothendieck and Delig ..."
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Cited by 791 (1 self)
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These are the notes for a course taught at the University of Michigan in 1989 and 1998. In comparison with my book, the emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes. The notes also discuss the proof of the Weil conjectures (Grothendieck
A comment on the WignerDysonMehta bulk universality conjecture for Wigner matrices
, 2012
"... Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices ..."
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Cited by 9 (2 self)
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Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our work [2].
Universality conjecture and results for a model of several coupled positivedefinite matrices. arXiv:1407.2597 [mathph
, 2014
"... Abstract. The paper contains two main parts: in the first part, we analyze the general case of p ≥ 2 matrices coupled in a chain subject to Cauchy interaction. Similarly to the ItzyksonZuber interaction model, the eigenvalues of the Cauchy chain form a multi level determinantal point process. We fi ..."
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Cited by 2 (0 self)
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asymptotics for the Cauchy biorthogonal polynomials when the support of the equilibrium measures contains the origin. As a result, we obtain a new family of universality classes for multilevel random determinantal point fields which include the Besselν universality for 1level and the MeijerG universality
Unipotent automorphic representations: conjectures
, 1989
"... In these notes, we shall attempt to make sense of the notions of semisimple and unipotent representations in the context of automorphic forms. Our goal is to formulate some conjectures, both local and global, which were originally motivated by the trace formula. Some of these conjectures were stated ..."
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Cited by 85 (3 self)
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stated less generally in lectures [2] at the University of Maryland. The present paper is an update of these lectures. We have tried to incorporate subsequent mathematical developments into a more comprehensive discussion of the conjectures. Even so, we have been forced for several reasons to work at a
A NEW REM CONJECTURE
, 2006
"... Abstract. We introduce here a new universality conjecture for levels of random Hamiltonians, in the same spirit as the local REM conjecture made by S. Mertens and H. Bauke. We establish our conjecture for a wide class of Gaussian and nonGaussian Hamiltonians, which include the pspin models, the Sh ..."
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Cited by 3 (0 self)
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Abstract. We introduce here a new universality conjecture for levels of random Hamiltonians, in the same spirit as the local REM conjecture made by S. Mertens and H. Bauke. We establish our conjecture for a wide class of Gaussian and nonGaussian Hamiltonians, which include the pspin models
On the LMO conjecture
"... Abstract. We give a proof of the LMO conjecture which say that for any simply connectd simple Lie group G, the LMO invariant of rational homology 3spheres recovers the perturvative invariant τ PG. By HabiroLe theorem, this implies that the LMO invariant is the universal quantum invariant of integr ..."
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Cited by 11 (2 self)
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Abstract. We give a proof of the LMO conjecture which say that for any simply connectd simple Lie group G, the LMO invariant of rational homology 3spheres recovers the perturvative invariant τ PG. By HabiroLe theorem, this implies that the LMO invariant is the universal quantum invariant
FeigenbaumCoulletTresser universality and Milnor's Hairiness Conjecture
, 1999
"... We prove the FeigenbaumCoulletTresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computerfree proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s c ..."
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Cited by 69 (7 self)
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We prove the FeigenbaumCoulletTresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computerfree proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s
Results 1  10
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1,479