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20
Maximum a posteriori estimation for multivariate gaussian mixture observations of markov chains
 IEEE Transactions on Speech and Audio Processing
, 1994
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Random matrices and random permutations
 Internat. Math. Res. Notices
, 2000
"... We prove the conjecture of Baik, Deift, and Johansson which says that with respect to the Plancherel measure on the set of partitions λ of n, the rows λ1,λ2,λ3,... of λ behave, suitably scaled, like the 1st, 2nd, 3rd, and so on eigenvalues of a Gaussian random Hermitian matrix as n → ∞. Our proof is ..."
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Cited by 77 (7 self)
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We prove the conjecture of Baik, Deift, and Johansson which says that with respect to the Plancherel measure on the set of partitions λ of n, the rows λ1,λ2,λ3,... of λ behave, suitably scaled, like the 1st, 2nd, 3rd, and so on eigenvalues of a Gaussian random Hermitian matrix as n → ∞. Our proof is based on an interplay between maps on surfaces and ramified coverings of the sphere. We also establish a connection of this problem with intersection theory on the moduli spaces of curves. 1
Central limit theorem for linear eigenvalue statistics of random matrices with . . .
, 2009
"... We consider n × n real symmetric and Hermitian Wigner random matrices n −1/2 W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n −1 X ∗ X with independent entries of m × n matrix X. Assuming first that the 4th cumulant (excess) κ4 of entries of W and X ..."
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Cited by 47 (1 self)
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We consider n × n real symmetric and Hermitian Wigner random matrices n −1/2 W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n −1 X ∗ X with independent entries of m × n matrix X. Assuming first that the 4th cumulant (excess) κ4 of entries of W and X is zero and that their 4th moments satisfy a Lindeberg type condition, we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem (CLT) as n → ∞, m → ∞, m/n → c ∈ [0, ∞) with the same variance as for Gaussian matrices if the test functions of statistics are smooth enough (essentially of the class C 5). This is done by using a simple “interpolation trick ” from the known results for the Gaussian matrices and the integration by parts, presented in the form of certain differentiation formulas. Then, by using a more elaborated version of the techniques, we prove the CLT in the case of nonzero excess of entries again for essentially C 5 test function. Here the variance of statistics contains an additional term proportional to κ4. The proofs of all limit theorems follow essentially the same scheme.
Pricing the American put option: a detailed convergence analysis for binomial models
 Journal of Economic Dynamics and Control
, 1998
"... Leisen and Reimer (1996) suggested to consider the order of convergence as a measure of convergence speed for European call options. In this paper we study in a first step the problem of determining the order of convergence in pricing American put options for several approaches in the literature. We ..."
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Cited by 8 (1 self)
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Leisen and Reimer (1996) suggested to consider the order of convergence as a measure of convergence speed for European call options. In this paper we study in a first step the problem of determining the order of convergence in pricing American put options for several approaches in the literature. We will then examine in detail extrapolation and the Control Variate technique for improving convergence and will explain their pitfalls. Since the investigation reveals the need for smooth converging models in order to get smaller initial errors, such a model is constructed. The different approaches are then tested: simulations exhibit up to 100 times smaller initial errors. � 1998 Published by Elsevier
Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices
, 2000
"... Abstract We use recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special bandgap scaling of the spectral surface of genus N so that the integrated density of states remains finite as N → ∞ ( ..."
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Cited by 7 (7 self)
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Abstract We use recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special bandgap scaling of the spectral surface of genus N so that the integrated density of states remains finite as N → ∞ (thermodynamic type limit). We prove existence of the limiting stationary ergodic process and associate it with the soliton turbulence. The phase space of the soliton turbulence is a onedimensional space with the random Poisson measure. The zero density limit of the soliton turbulence coincides with the Frish Lloyd potential of the quantum theory of disordered systems. 1
Decoherence Produces Coherent States: An Explicit Proof For Harmonic Chains
, 1994
"... We study the behavior of infinite systems of coupled harmonic oscillators as the time t ! 1, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This shows that generalized coherent states tend to be produc ..."
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Cited by 5 (0 self)
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We study the behavior of infinite systems of coupled harmonic oscillators as the time t ! 1, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This shows that generalized coherent states tend to be produced naturally. A sufficient condition for this to happen is shown to be that the spectral function is analytic and nonlinear. For a chain of coupled oscillators, the nonlinearity requirement means that waves must be dispersive, so that localized wavepackets become suppressed. Virtually all harmonic heatbath models in the literature satisfy this constraint, and we have good reason to believe that coherent states and their generalizations are not merely a useful analytical tool, but that nature is indeed full of them. Standard proofs of the CLT rely heavily on the fact that probability densities are nonnegative. Although the CLT is generally not applicable if the densities are allowed to take negative values, we show that a CLT does indeed hold for a special class of such functions. We find that, intriguingly, nature has arranged things so that all Wigner functions belong to this class. PACS Codes: 5.30.d, 5.30.ch, 2.50.+s, 3.65.w y Published in Phys. Rev. E, 50, 2538 (1994) 1 I.
Lyapunov exponents in continuum BernoulliAnderson models
 in Operator Methods in Ordinary and Partial Differential Equations (Stockholm, 2000 ), 121–130, Oper. Theory Adv. Appl., 132
, 2002
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NONLINEAR TRAJECTORY NAVIGATION
, 2007
"... To my parents. ii ACKNOWLEDGEMENTS During the past five years at Michigan so many things have happened and there are so many people to thank. First and foremost, it’s my parents who have encouraged me to pursue PhD studies. I thank them for their encouragements and supports throughout my academic ca ..."
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Cited by 2 (0 self)
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To my parents. ii ACKNOWLEDGEMENTS During the past five years at Michigan so many things have happened and there are so many people to thank. First and foremost, it’s my parents who have encouraged me to pursue PhD studies. I thank them for their encouragements and supports throughout my academic career. To Prof. Daniel Scheeres, who has been my PhD advisor and a lifelong mentor: it is his guidance and help that made this dissertation exist. I want to thank him, but no matter how much say here, I would not feel I have said enough. He has taught me the concept of how much one can owe someone so much. Hence, instead of thanking him, I promise that I will do the same as I have learned from him. Thank you for teaching me this valuable lesson! To Sophia Lim, who has patiently encouraged my studies and gave me the motivation for completing this dissertation: I thank you. Also, I am very grateful
An ”eulerian ” approach to a class of matching problems
"... Abstract. We study a card game called He Loves Me, He Loves Me Not ((HLM)2N), which can be considered as a generalization of the classical games Treize and Mousetrap. We give some results by a theoretical point of view and by a numerical one, by means of Monte Carlo simulations. Furthermore, we intr ..."
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Cited by 1 (1 self)
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Abstract. We study a card game called He Loves Me, He Loves Me Not ((HLM)2N), which can be considered as a generalization of the classical games Treize and Mousetrap. We give some results by a theoretical point of view and by a numerical one, by means of Monte Carlo simulations. Furthermore, we introduce a new technique which allows us to obtain the best result at least for French card decks (52 cards with 4 seeds). This technique allows us to answer to some open questions related to the game Mousetrap.
Artificial neural networks as approximators of stochastic processes
 Neural Networks
, 1999
"... Artificial (or biological) Neural Networks must be able to form by learning internal memory of the environment to determine decisions and subsequent actions to stimuli. By assuming that environment is essentially stochastic it follows that the mathematical framework for learning information from env ..."
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Cited by 1 (0 self)
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Artificial (or biological) Neural Networks must be able to form by learning internal memory of the environment to determine decisions and subsequent actions to stimuli. By assuming that environment is essentially stochastic it follows that the mathematical framework for learning information from environment is the theory of stochastic processes approximation. The aim of this paper is to show that classes of neural networks capable of approximating stochastic processes exist. 1