TY - JOUR
T1 - Spectral Fluctuations for Schrödinger Operators with a Random Decaying Potential
AU - Breuer, Jonathan
AU - Grinshpon, Yoel
AU - White, Moshe J.
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021/11
Y1 - 2021/11
N2 - We study fluctuations of polynomial linear statistics for discrete Schrödinger operators with a random decaying potential. We describe a decomposition of the space of polynomials into a direct sum of three subspaces determining the growth rate of the variance of the corresponding linear statistic. In particular, each one of these subspaces defines a unique critical value for the decay-rate exponent, above which the random variable has a limit that is sensitive to the underlying distribution and below which the random variable has asymptotically Gaussian fluctuations.
AB - We study fluctuations of polynomial linear statistics for discrete Schrödinger operators with a random decaying potential. We describe a decomposition of the space of polynomials into a direct sum of three subspaces determining the growth rate of the variance of the corresponding linear statistic. In particular, each one of these subspaces defines a unique critical value for the decay-rate exponent, above which the random variable has a limit that is sensitive to the underlying distribution and below which the random variable has asymptotically Gaussian fluctuations.
UR - http://www.scopus.com/inward/record.url?scp=85117075909&partnerID=8YFLogxK
U2 - 10.1007/s00023-021-01082-9
DO - 10.1007/s00023-021-01082-9
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AN - SCOPUS:85117075909
SN - 1424-0637
VL - 22
SP - 3763
EP - 3794
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 11
ER -