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Permanental Random Variables, M-Matrices and α-Permanents

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High Dimensional Probability VII

Part of the book series: Progress in Probability ((PRPR,volume 71))

Abstract

We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.

Mathematics Subject Classification (2010). Primary 15B99, 60E07, 60J55; Secondary 60G17

Research of the second author was supported by grants from the National Science Foundation, PSCCUNY and grant number 208494 from the Simons Foundation.

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References

  1. A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. Classics in Applied Mathematics (SIAM, Philadelphia, 1994)

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  2. M.B. Marcus, J. Rosen, Conditions for permanental processes to be unbounded. Annals of Probability (to appear)

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  3. D. Vere-Jones, Alpha-permanents. New Zealand J. Math. 26, 125–149 (1997)

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Author information

Authors and Affiliations

  1. CUNY Graduate Center, 253 West 73rd St., Apt. 2E, New York, NY, 10023, USA

    Michael B. Marcus

  2. Department of Mathematics, College of Staten Island, CUNY, 2800 Victory Boulevard, Staten Island, NY, 10314, USA

    Jay Rosen

Authors
  1. Michael B. Marcus
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  2. Jay Rosen
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Corresponding author

Correspondence to Michael B. Marcus .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, Georgia, USA

    Christian Houdré

  2. University of Delaware, Department of Applied Economics and Stat University of Delaware, Newark, Delaware, USA

    David M. Mason

  3. Centre national de la recherche scientifique, Laboratoire J.A. Dieudonné, Université Côte d’Azur, Nice, France

    Patricia Reynaud-Bouret

  4. Department of Mathematics, University of Tennessee Department of Mathematics, Knoxville, Tennessee, USA

    Jan Rosiński

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© 2016 Springer International Publishing Switzerland

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Marcus, M.B., Rosen, J. (2016). Permanental Random Variables, M-Matrices and α-Permanents. In: Houdré, C., Mason, D., Reynaud-Bouret, P., Rosiński, J. (eds) High Dimensional Probability VII. Progress in Probability, vol 71. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40519-3_16

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