The Experts below are selected from a list of 13119 Experts worldwide ranked by ideXlab platform
Grigori Olshanski - One of the best experts on this subject based on the ideXlab platform.
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the quasi Invariance Property for the gamma kernel determinantal measure
Advances in Mathematics, 2011Co-Authors: Grigori OlshanskiAbstract:Abstract The Gamma kernel is a projection kernel of the form ( A ( x ) B ( y ) − B ( x ) A ( y ) ) / ( x − y ) , where A and B are certain functions on the one-dimensional lattice expressed through Euler's Γ-function. The Gamma kernel depends on two continuous parameters; its principal minors serve as the correlation functions of a determinantal probability measure P defined on the space of infinite point configurations on the lattice. As was shown earlier [A. Borodin, G. Olshanski, Adv. Math. 194 (2005) 141–202, arXiv:math-ph/0305043 ], P describes the asymptotics of certain ensembles of random partitions in a limit regime. Theorem: The determinantal measure P is quasi-invariant with respect to finitary permutations of the nodes of the lattice. This result is motivated by an application to a model of infinite particle stochastic dynamics.
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the quasi Invariance Property for the gamma kernel determinantal measure
arXiv: Probability, 2009Co-Authors: Grigori OlshanskiAbstract:The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the one-dimensional lattice expressed through Euler's Gamma function. The Gamma kernel depends on two continuous parameters; its principal minors serve as the correlation functions of a determinantal probability measure P defined on the space of infinite point configurations on the lattice. As was shown earlier (Borodin and Olshanski, Advances in Math. 194 (2005), 141-202; arXiv:math-ph/0305043), P describes the asymptotics of certain ensembles of random partitions in a limit regime. Theorem: The determinantal measure P is quasi-invariant with respect to finitary permutations of the nodes of the lattice. This result is motivated by an application to a model of infinite particle stochastic dynamics.
Fernando Vidal - One of the best experts on this subject based on the ideXlab platform.
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the directional distance function and the translation Invariance Property
Omega-international Journal of Management Science, 2016Co-Authors: Juan Aparicio, Jesus T Pastor, Fernando VidalAbstract:Abstract Recently, in a Data Envelopment Analysis (DEA) framework, Fare and Grosskopf [15] argued that the input directional distance function is invariant to affine data transformations under variable returns to scale (VRS), which includes, as a particular case, the Property of translation Invariance. In this paper we show that, depending on the directional vector used, the translation Invariance may fail. In order to identify the directional distance functions (DDFs) that are translation invariant under VRS, we establish a necessary and sufficient condition that the directional vector must fulfill. As a consequence, we identify the characteristics that the DDFs should verify to be translation invariant. We additionally show some distinguished members that satisfy the aforementioned condition. We finally give several examples of DDFs, including input and output DDFs, which are not translation invariant.
Juan Aparicio - One of the best experts on this subject based on the ideXlab platform.
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the directional distance function and the translation Invariance Property
Omega-international Journal of Management Science, 2016Co-Authors: Juan Aparicio, Jesus T Pastor, Fernando VidalAbstract:Abstract Recently, in a Data Envelopment Analysis (DEA) framework, Fare and Grosskopf [15] argued that the input directional distance function is invariant to affine data transformations under variable returns to scale (VRS), which includes, as a particular case, the Property of translation Invariance. In this paper we show that, depending on the directional vector used, the translation Invariance may fail. In order to identify the directional distance functions (DDFs) that are translation invariant under VRS, we establish a necessary and sufficient condition that the directional vector must fulfill. As a consequence, we identify the characteristics that the DDFs should verify to be translation invariant. We additionally show some distinguished members that satisfy the aforementioned condition. We finally give several examples of DDFs, including input and output DDFs, which are not translation invariant.
Bo Zhang - One of the best experts on this subject based on the ideXlab platform.
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inverse acoustic scattering with phaseless far field data uniqueness phase retrieval and direct sampling methods
Siam Journal on Imaging Sciences, 2019Co-Authors: Xia Ji, Bo ZhangAbstract:The well-known translation Invariance Property of the phaseless far field patterns with incident plane waves make it is impossible to reconstruct the location of the underlying scatterers even for ...
Pawel Pasteczka - One of the best experts on this subject based on the ideXlab platform.
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scales of quasi arithmetic means determined by an Invariance Property
Journal of Difference Equations and Applications, 2015Co-Authors: Pawel PasteczkaAbstract:It is well known that if {𝒫t}t∈R denotes the set of power means, then the mapping R∋t↦𝒫t(v)∈(min v,max v) is both 1 − 1 and onto for any non-constant sequence v=(v1,…,vn) of positive numbers. Briefly, the family of power means is a scale. If I is an interval and f:I→R is a continuous, strictly monotone function, then f−1((1/n)∑f(vi)) is a natural generalization of the power mean, so called quasi-arithmetic mean generated by f. A famous theorem says that the only homogeneous, quasi-arithmetic means are power means. We prove that, upon replacing the homogeneity requirement by an invariant-type axiom, one gets a family of quasi-arithmetic means building up a scale, too.
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scales of quasi arithmetic means determined by Invariance Property
arXiv: Classical Analysis and ODEs, 2014Co-Authors: Pawel PasteczkaAbstract:It is well known that if $\mathcal{P}_t$ denotes a set of power means then the mapping $\mathbb{R} \ni t \mapsto \mathcal{P}_t(v) \in (\min v, \max v)$ is both 1-1 and onto for any non-constant sequence $v = (v_1,\dots,\,v_n)$ of positive numbers. Shortly: the family of power means is a scale. If $I$ is an interval and $f \colon I \rightarrow \mathbb{R}$ is a continuous, strictly monotone function then $f^{-1}(\tfrac{1}{n} \sum f(v_i))$ is a natural generalization of power means, so called quasi-arithmetic mean generated by $f$. A famous folk theorem says that the only homogeneous, quasi-a\-rith\-me\-tic means are power means. We prove that, upon replacing the homogeneity requirement by an invariant-type axiom, one gets a family of quasi-arithmetic means building up a scale, too.
