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Genus one correlation to multicut matrix model solutions L. Chekhov 1
, 2004
"... We calculate genus one corrections to Hermitian onematrix model solution with arbitrary number of cuts directly from the loop equation confirming the answer previously obtained from algebrogeometrical considerations and generalizing it to the case of arbitrary potentials. 1 ..."
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We calculate genus one corrections to Hermitian onematrix model solution with arbitrary number of cuts directly from the loop equation confirming the answer previously obtained from algebrogeometrical considerations and generalizing it to the case of arbitrary potentials. 1
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n
The Nonstochastic Multiarmed Bandit Problem
 SIAM JOURNAL OF COMPUTING
, 2002
"... In the multiarmed bandit problem, a gambler must decide which arm of K nonidentical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the tradeoff between exploration (trying out ..."
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Cited by 491 (34 self)
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In the multiarmed bandit problem, a gambler must decide which arm of K nonidentical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the tradeoff between exploration (trying
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 427 (36 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
Macroscopic Loop Amplitudes in the MultiCut TwoMatrix Models
, 2009
"... Multicut critical points and their macroscopic loop amplitudes are studied in the multicut twomatrix models, based on an extension of the prescription developed by Daul, Kazakov and Kostov. After identifying possible critical points and potentials in the multicut matrix models, we calculate the ..."
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Cited by 4 (3 self)
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Multicut critical points and their macroscopic loop amplitudes are studied in the multicut twomatrix models, based on an extension of the prescription developed by Daul, Kazakov and Kostov. After identifying possible critical points and potentials in the multicut matrix models, we calculate
Loop equations and the topological phase of multicut matrix models
 Int. J. Mod. Phys. A
, 1992
"... We study the double scaling limit of mKdV type, realized in the twocut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of 2 × 2 matrices. We derive from it loop equation ..."
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Cited by 20 (1 self)
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We study the double scaling limit of mKdV type, realized in the twocut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of 2 × 2 matrices. We derive from it loop
Asymptotic expansion of β matrix models in the multicut regime
, 2013
"... We push further our study of the allorder asymptotic expansion in β matrix models with a confining, offcritical potential, in the regime where the support of the equilibrium measure is a reunion of segments. We first address the case where the filling fractions of those segments are fixed, and show ..."
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Cited by 7 (1 self)
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, and show the existence of a 1{N expansion to all orders. Then, we study the asymptotic of the sum over filling fractions, in order to obtain the full asymptotic expansion for the initial problem in the multicut regime. We describe the application of our results to study the allorder small dispersion
The Resurgence of Instantons: Multi–Cuts Stokes Phases and the Painleve ́ II Equation
"... Abstract: Resurgent transseries have recently been shown to be a very powerful construction in order to completely describe nonperturbative phenomena in both matrix models and topological or minimal strings. These solutions encode the full nonperturbative content of a given gauge or string theory, w ..."
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Cited by 1 (0 self)
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study of Stokes phases associated to multi–cuts solutions of generic matrix models, constructing nonperturbative solutions for their free energies and exploring the asymptotic large–order behavior around distinct multi–instanton sectors. Explicit formulae are presented for the Z2 symmetric two–cuts set
Preprint typeset in JHEP style PAPER VERSION CERNPHTH/2008186 Multi–Instantons and Multi–Cuts
, 809
"... Abstract: We discuss various aspects of multi–instanton configurations in generic multi–cut matrix models. Explicit formulae are presented in the two–cut case and, in particular, we obtain general formulae for multi–instanton amplitudes in the one–cut matrix model case as a degeneration of the two–c ..."
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Abstract: We discuss various aspects of multi–instanton configurations in generic multi–cut matrix models. Explicit formulae are presented in the two–cut case and, in particular, we obtain general formulae for multi–instanton amplitudes in the one–cut matrix model case as a degeneration of the two–cut
Fractional supersymmetric Liouville theory and the multicut matrix models
 Nucl. Phys. B
"... We argue that the noncritical version of the kfractional superstring theory can be described with the kcut critical points of the matrix models. In particular we show that, from the spectrum structure of fractional superLiouville theory, (p, q) minimal fractional superstrings live in the Zksymm ..."
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Cited by 7 (4 self)
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We argue that the noncritical version of the kfractional superstring theory can be described with the kcut critical points of the matrix models. In particular we show that, from the spectrum structure of fractional superLiouville theory, (p, q) minimal fractional superstrings live in the Zk
Results 1  10
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4,603