메뉴 건너뛰기




Volumn 375, Issue 2, 2007, Pages 499-517

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

Author keywords

Entropic uncertainty relation; Multivariate Student t and Student r distributions; R nyi Shannon entropy

Indexed keywords

ASYMPTOTIC STABILITY; ENTROPY; MULTIVARIABLE SYSTEMS; NUMERICAL METHODS; VECTORS;

EID: 33845410718     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.09.019     Document Type: Article
Times cited : (60)

References (51)
  • 2
    • 0007506136 scopus 로고
    • Uncertainty inequalities for Hankel transforms
    • Bowie P.C. Uncertainty inequalities for Hankel transforms. SIAM J. Math. Anal. 2 4 (1971) 601-606
    • (1971) SIAM J. Math. Anal. , vol.2 , Issue.4 , pp. 601-606
    • Bowie, P.C.1
  • 5
    • 0000617016 scopus 로고
    • Uncertainty relations for information entropy in wave mechanics
    • Bialynicki-Birula I., and Mycielski J. Uncertainty relations for information entropy in wave mechanics. Commun. Math. Phys. 44 2 (1975) 129-132
    • (1975) Commun. Math. Phys. , vol.44 , Issue.2 , pp. 129-132
    • Bialynicki-Birula, I.1    Mycielski, J.2
  • 6
    • 84987059628 scopus 로고
    • Maximization of atomic information-entropy sum in configuration and momentum spaces
    • Gadre S.R., and Bendale R.D. Maximization of atomic information-entropy sum in configuration and momentum spaces. Int. J. Quantum Chem. 28 2 (1985) 311-314
    • (1985) Int. J. Quantum Chem. , vol.28 , Issue.2 , pp. 311-314
    • Gadre, S.R.1    Bendale, R.D.2
  • 7
    • 0039896109 scopus 로고    scopus 로고
    • Information theoretic approach to statistical properties of multivariate Cauchy-Lorentz distribution
    • Abe S., and Rajagopal A.K. Information theoretic approach to statistical properties of multivariate Cauchy-Lorentz distribution. J. Phys. A 34 42 (2001) 8727-8731
    • (2001) J. Phys. A , vol.34 , Issue.42 , pp. 8727-8731
    • Abe, S.1    Rajagopal, A.K.2
  • 9
    • 0000898117 scopus 로고
    • Inequalities in Fourier analysis
    • Beckner W. Inequalities in Fourier analysis. Ann. Math. 102 1 (1975) 159-182
    • (1975) Ann. Math. , vol.102 , Issue.1 , pp. 159-182
    • Beckner, W.1
  • 10
    • 33845401900 scopus 로고    scopus 로고
    • A. Rényi, On measures of entropy and information, in: Proceeding of the 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, 1961, pp. 547-561.
  • 11
    • 0033733712 scopus 로고    scopus 로고
    • Statistical mechanics based on Rényi entropy
    • Lenzi E.K., Mendes R.S., and da Silva L.R. Statistical mechanics based on Rényi entropy. Physica A 280 3-4 (2000) 337-345
    • (2000) Physica A , vol.280 , Issue.3-4 , pp. 337-345
    • Lenzi, E.K.1    Mendes, R.S.2    da Silva, L.R.3
  • 12
    • 3142672769 scopus 로고    scopus 로고
    • The world according to Rényi: thermodynamics of multifractal systems
    • Jizba P., and Arimitsu T. The world according to Rényi: thermodynamics of multifractal systems. Ann. Phys. 312 1 (2004) 17-59
    • (2004) Ann. Phys. , vol.312 , Issue.1 , pp. 17-59
    • Jizba, P.1    Arimitsu, T.2
  • 13
    • 19444382575 scopus 로고    scopus 로고
    • Extensive Rényi statistics from non-extensive entropy
    • Parvan A.S., and Biró T.S. Extensive Rényi statistics from non-extensive entropy. Phys. Lett. A 340 5-6 (2005) 375-387
    • (2005) Phys. Lett. A , vol.340 , Issue.5-6 , pp. 375-387
    • Parvan, A.S.1    Biró, T.S.2
  • 16
    • 13444256399 scopus 로고    scopus 로고
    • Sensor management using an active sensing approach
    • Kreucher C., Kastella K., and Hero III A.O. Sensor management using an active sensing approach. Signal Process. 85 3 (2005) 607-624
    • (2005) Signal Process. , vol.85 , Issue.3 , pp. 607-624
    • Kreucher, C.1    Kastella, K.2    Hero III, A.O.3
  • 19
    • 0001287029 scopus 로고
    • Generalized entropic uncertainty relations
    • Maassen H., and Uffink J.B.M. Generalized entropic uncertainty relations. Phys. Rev. Lett. 60 12 (1988) 1103-1106
    • (1988) Phys. Rev. Lett. , vol.60 , Issue.12 , pp. 1103-1106
    • Maassen, H.1    Uffink, J.B.M.2
  • 20
    • 0002347030 scopus 로고
    • The Sobolev inequality and the Tsallis entropic uncertainty relation
    • Rajagopal A.K. The Sobolev inequality and the Tsallis entropic uncertainty relation. Phys. Lett. A 205 1 (1995) 32-36
    • (1995) Phys. Lett. A , vol.205 , Issue.1 , pp. 32-36
    • Rajagopal, A.K.1
  • 21
    • 0034347775 scopus 로고    scopus 로고
    • Generalized position and momentum Tsallis entropies
    • Ghosh A., and Chaudhuri P. Generalized position and momentum Tsallis entropies. Int. J. Theoret. Phys. 39 10 (2000) 2423-2437
    • (2000) Int. J. Theoret. Phys. , vol.39 , Issue.10 , pp. 2423-2437
    • Ghosh, A.1    Chaudhuri, P.2
  • 22
    • 0032299256 scopus 로고    scopus 로고
    • The role of constraints within generalized nonextensive statistics
    • Tsallis C., Mendes R.M., and Plastino A.R. The role of constraints within generalized nonextensive statistics. Physica A 261 2 (1998) 534-554
    • (1998) Physica A , vol.261 , Issue.2 , pp. 534-554
    • Tsallis, C.1    Mendes, R.M.2    Plastino, A.R.3
  • 23
    • 0033242934 scopus 로고    scopus 로고
    • Nonextensive statistics: theoretical, experimental and computational evidences and connections
    • Tsallis C. Nonextensive statistics: theoretical, experimental and computational evidences and connections. Brazilian J. Phys. 29 1 (1999) 1-35
    • (1999) Brazilian J. Phys. , vol.29 , Issue.1 , pp. 1-35
    • Tsallis, C.1
  • 24
    • 33845464468 scopus 로고    scopus 로고
    • I. Bialynicki-Birula, Formulation of the uncertainty relations in terms of the Rényi entropies, arXiv:quant-ph/0608116.
  • 25
    • 0000201926 scopus 로고
    • Gaussian kernels have only Gaussian maximizers
    • Lieb E.H. Gaussian kernels have only Gaussian maximizers. Invent. Math. 102 1 (1990) 179-208
    • (1990) Invent. Math. , vol.102 , Issue.1 , pp. 179-208
    • Lieb, E.H.1
  • 26
    • 4344595247 scopus 로고    scopus 로고
    • An entropy-based uncertainty principle for a locally compact abelian group
    • Özaydin M., and Przebinda T. An entropy-based uncertainty principle for a locally compact abelian group. J. Functional Anal. 215 1 (2004) 241-252
    • (2004) J. Functional Anal. , vol.215 , Issue.1 , pp. 241-252
    • Özaydin, M.1    Przebinda, T.2
  • 27
    • 0015672091 scopus 로고
    • Estimation and decision for linear systems with elliptical random processes
    • Chu K.-C. Estimation and decision for linear systems with elliptical random processes. IEEE Trans. Autom. Control 18 5 (1973) 499-505
    • (1973) IEEE Trans. Autom. Control , vol.18 , Issue.5 , pp. 499-505
    • Chu, K.-C.1
  • 30
    • 0002834599 scopus 로고
    • The use of the Hankel transform in statistics I. General theory and examples
    • Lord R. The use of the Hankel transform in statistics I. General theory and examples. Biometrika 41 1/2 (1954) 44-55
    • (1954) Biometrika , vol.41 , Issue.1-2 , pp. 44-55
    • Lord, R.1
  • 35
    • 0002233478 scopus 로고
    • Applications of "Student's" distributions
    • Fisher R.A. Applications of "Student's" distributions. Metron 5 3 (1925) 90-104
    • (1925) Metron , vol.5 , Issue.3 , pp. 90-104
    • Fisher, R.A.1
  • 36
    • 0000753064 scopus 로고
    • Student's t-test under symmetry conditions
    • Efron B. Student's t-test under symmetry conditions. J. Amer. Stat. Assoc. 64 328 (1969) 1278-1302
    • (1969) J. Amer. Stat. Assoc. , vol.64 , Issue.328 , pp. 1278-1302
    • Efron, B.1
  • 37
    • 3042811700 scopus 로고    scopus 로고
    • About closedness by convolution of the Tsallis maximizers
    • Vignat C., Hero III A.O., and Costa J.A. About closedness by convolution of the Tsallis maximizers. Physica A 340 1-3 (2004) 147-152
    • (2004) Physica A , vol.340 , Issue.1-3 , pp. 147-152
    • Vignat, C.1    Hero III, A.O.2    Costa, J.A.3
  • 38
    • 18744376509 scopus 로고    scopus 로고
    • Maximum Rényi entropy principle for systems with power-law Hamiltonians
    • Bashkirov A.G. Maximum Rényi entropy principle for systems with power-law Hamiltonians. Phys. Rev. Lett. 93 13 (2004) 130601
    • (2004) Phys. Rev. Lett. , vol.93 , Issue.13 , pp. 130601
    • Bashkirov, A.G.1
  • 40
    • 0040809279 scopus 로고    scopus 로고
    • A multivariate and asymmetric generalization of Laplace distribution
    • Kozubowski T.J., and Podgórski K. A multivariate and asymmetric generalization of Laplace distribution. Comput. Statist. 15 4 (2000) 531-540
    • (2000) Comput. Statist. , vol.15 , Issue.4 , pp. 531-540
    • Kozubowski, T.J.1    Podgórski, K.2
  • 41
    • 33845422680 scopus 로고    scopus 로고
    • S. Kotz, T.J. Kozubowski, K. Podgórski, An asymmetric multivariate Laplace distribution, Technical Report 367, Department of Statistics and Applied Probabilities, University of California at Santa Barbara, USA, 2000.
  • 42
    • 0032385158 scopus 로고    scopus 로고
    • A multivariate generalized Laplace distribution
    • Ernst M.D. A multivariate generalized Laplace distribution. Comput. Statist. 13 2 (1998) 227-232
    • (1998) Comput. Statist. , vol.13 , Issue.2 , pp. 227-232
    • Ernst, M.D.1
  • 43
    • 35248835962 scopus 로고    scopus 로고
    • J.A. Costa, A.O. Hero III, C. Vignat, On solutions to multivariate maximum α-entropy problems, in: A. Rangarajan, M.A.T. Figueiredo, J. Zerubia (Eds.), Fourth International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Lecture Notes in Computer Sciences, vol. 2683, Springer, Lisbon, Portugal, 2003, pp. 211-226.
  • 44
    • 33845382058 scopus 로고    scopus 로고
    • On the momentum distribution of molecules of an ideal gas
    • Matolcsi T., Kristóf J., and Székely M. On the momentum distribution of molecules of an ideal gas. Publ. Appl. Anal. 7 (1996) 1-14
    • (1996) Publ. Appl. Anal. , vol.7 , pp. 1-14
    • Matolcsi, T.1    Kristóf, J.2    Székely, M.3
  • 45
    • 0037737627 scopus 로고    scopus 로고
    • Analysis of signals in the Fisher-Shannon information plane
    • Vignat C., and Bercher J.-F. Analysis of signals in the Fisher-Shannon information plane. Phys. Lett. A 312 1-2 (2003) 27-33
    • (2003) Phys. Lett. A , vol.312 , Issue.1-2 , pp. 27-33
    • Vignat, C.1    Bercher, J.-F.2
  • 47
    • 33845426084 scopus 로고    scopus 로고
    • N. Mukhopadhyay, Probability and Statistical Inference, In: Statistics: Textbooks and Monographs, fifth ed., vol. 162, Marcel Dekker, New York, 2000.
  • 48
    • 0000599192 scopus 로고
    • A dozen de Finetti-style results in search of a theory
    • Diaconis P., and Freedman D. A dozen de Finetti-style results in search of a theory. Ann. Inst. Henri Poincaré Probab. Stat. 23 Suppl. to no. 2 (1987) 397-423
    • (1987) Ann. Inst. Henri Poincaré Probab. Stat. , vol.23 , Issue.SUPPL. to 2 , pp. 397-423
    • Diaconis, P.1    Freedman, D.2
  • 49
    • 0141529857 scopus 로고    scopus 로고
    • Entropy and a generalisation of "Poincaré's observation"
    • Johnson O. Entropy and a generalisation of "Poincaré's observation". Mathematical Proc. Cambridge Philos. Soc. 135 2 (2003) 375-384
    • (2003) Mathematical Proc. Cambridge Philos. Soc. , vol.135 , Issue.2 , pp. 375-384
    • Johnson, O.1
  • 50
    • 0035305311 scopus 로고    scopus 로고
    • Relative entropy: free energy associated with equilibrium fluctuations and nonequilibrium deviations
    • Qian H. Relative entropy: free energy associated with equilibrium fluctuations and nonequilibrium deviations. Phys. Rev. E 63 4 (2001) 042103
    • (2001) Phys. Rev. E , vol.63 , Issue.4 , pp. 042103
    • Qian, H.1
  • 51
    • 24144434076 scopus 로고    scopus 로고
    • Relative entropy and efficiency measure for diffusion-mediated transport process
    • Filliger R., and Hongler M.O. Relative entropy and efficiency measure for diffusion-mediated transport process. J. Phys. A 38 6 (2005) 1247-1255
    • (2005) J. Phys. A , vol.38 , Issue.6 , pp. 1247-1255
    • Filliger, R.1    Hongler, M.O.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.