Electronic Journal of Probability

Erratum to ``Number Variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric $\alpha$-stable processes"

Ben Hambly and Lisa Jones

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Abstract

In our original paper, we provide an expression for the variance of the counting functions associated with the spatial particle configurations formed by infinite systems of independent symmetric alpha-stable processes. The formula (2.3) of the original paper, is in fact the correct expression for the expected conditional number variance. This is equal to the full variance when L is a positive integer multiple of the parameter a but, in general, the full variance has an additional bounded fluctuating term. The main results of the paper still hold for the full variance itself, although some of the proofs require modification in order to incorporate this change.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 37, 1074-1079.

Dates
Accepted: 26 May 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819498

Digital Object Identifier
doi:10.1214/EJP.v14-658

Mathematical Reviews number (MathSciNet)
MR2506125

Zentralblatt MATH identifier
1196.60088

Subjects
Primary: 60G52: Stable processes
Secondary: 60G15: Gaussian processes

Keywords
Number variance symmetric $\alpha$-stable processes controlled variability Gaussian fluctuations functional limits long memory Gaussian processes fractional Brownian motion

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Hambly, Ben; Jones, Lisa. Erratum to ``Number Variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric $\alpha$-stable processes". Electron. J. Probab. 14 (2009), paper no. 37, 1074--1079. doi:10.1214/EJP.v14-658. https://projecteuclid.org/euclid.ejp/1464819498


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References

  • Ben Hambly and Liza Jones. Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric alpha-stable processes. Electron. J. Probab., 12:no. 30, 862–887 (electronic), 2007.
  • K. Johansson. Determinantal processes with number variance saturation. Comm. Math. Phys., 252(1-3):111–148, 2004.