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Gap probabilities and applications to geometry and random topology
"... Abstract. We give an exact formula for the value of the derivative at zero of the gap probability fβ,n in finite Gaussian βensembles (β = 1, 2, 4). As n goes to infinity our computation provides: f ′β,n(0) ∼ − ..."
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Cited by 4 (4 self)
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Abstract. We give an exact formula for the value of the derivative at zero of the gap probability fβ,n in finite Gaussian βensembles (β = 1, 2, 4). As n goes to infinity our computation provides: f ′β,n(0) ∼ −
CLAN STRUCTURE ANALYSIS AND RAPIDITY GAP PROBABILITY
, 1994
"... Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applie ..."
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are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at Tevatron and Hera.
Gap Probabilities in NonHermitian Random Matrix Theory
, 901
"... We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with both complex (β = 2) or quaternion real (β = 4) matrix elem ..."
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Cited by 3 (1 self)
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We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with both complex (β = 2) or quaternion real (β = 4) matrix
Discrete gap probabilities and discrete Painlevé equations
 DUKE MATH J
, 2003
"... We prove that Fredholm determinants of the form det(1 − Ks), where Ks is the restriction of either the discrete Bessel kernel or the discrete 2F1kernel to {s, s + 1,...}, can be expressed, respectively, through solutions of discrete Painlevé II (dPII) and Painlevé V (dPV) equations. These Fredholm ..."
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Cited by 29 (6 self)
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We prove that Fredholm determinants of the form det(1 − Ks), where Ks is the restriction of either the discrete Bessel kernel or the discrete 2F1kernel to {s, s + 1,...}, can be expressed, respectively, through solutions of discrete Painlevé II (dPII) and Painlevé V (dPV) equations. These Fredholm determinants can also be viewed as distribution functions of the first part of the random partitions distributed according to a Poissonized Plancherel measure and a zmeasure, or as normalized Toeplitz determinants with symbols eη(ζ +ζ −1) and (1 + ξζ)
τFUNCTION EVALUATION OF GAP PROBABILITIES IN ORTHOGONAL AND SYMPLECTIC MATRIX ENSEMBLES
, 2002
"... It has recently been emphasized that all known exact evaluations of gap probabilities for classical unitary matrix ensembles are in fact τfunctions for certain Painlevé systems. We show that all exact evaluations of gap probabilities for classical orthogonal matrix ensembles, either known or deriva ..."
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Cited by 12 (4 self)
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It has recently been emphasized that all known exact evaluations of gap probabilities for classical unitary matrix ensembles are in fact τfunctions for certain Painlevé systems. We show that all exact evaluations of gap probabilities for classical orthogonal matrix ensembles, either known
PRELIMINARY VERSION GAP PROBABILITIES FOR THE CARDINAL SINE
"... Abstract. We study the zero set of random analytic functions generated by a sum of the cardinal sine functions that form an orthogonal basis for the PaleyWiener space. As a model case, we consider realvalued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero i ..."
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Abstract. We study the zero set of random analytic functions generated by a sum of the cardinal sine functions that form an orthogonal basis for the PaleyWiener space. As a model case, we consider realvalued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero
The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation
"... We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard TracyWidom distribution, while the numerator is the Fredholm determinant of a very explicit kernel constructed with Airy functions and exponentials. The formula allows ..."
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Cited by 3 (0 self)
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We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard TracyWidom distribution, while the numerator is the Fredholm determinant of a very explicit kernel constructed with Airy functions and exponentials. The formula allows
Estimating Wealth Effects without Expenditure Data— or Tears
 Policy Research Working Paper 1980, The World
, 1998
"... Abstract: We use the National Family Health Survey (NFHS) data collected in Indian states in 1992 and 1993 to estimate the relationship between household wealth and the probability a child (aged 6 to 14) is enrolled in school. A methodological difficulty to overcome is that the NFHS, modeled closely ..."
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Cited by 871 (16 self)
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Abstract: We use the National Family Health Survey (NFHS) data collected in Indian states in 1992 and 1993 to estimate the relationship between household wealth and the probability a child (aged 6 to 14) is enrolled in school. A methodological difficulty to overcome is that the NFHS, modeled
Pivoted Document Length Normalization
 SIGIR'96
, 1996
"... Automatic information retrieval systems have to deal with documents of varying lengths in a text collection. Document length normalization is used to fairly retrieve documents of all lengths. In this study, we ohserve that a normalization scheme that retrieves documents of all lengths with similar c ..."
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Cited by 477 (16 self)
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different collections. We present pivoted normalization, a technique that can be used to modify any normalization function thereby reducing the gap between the relevance and the retrieval probabilities. Training pivoted normalization on one collection, we can successfully use it on other (new) text
Results 1  10
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