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.
"Erratum to ``Number Variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric $\alpha$-stable processes"." Electron. J. Probab. 14 1074 - 1079, 2009. https://doi.org/10.1214/EJP.v14-658