TY - JOUR
T1 - The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles
AU - Breuer, Jonathan
AU - Duits, Maurice
PY - 2014/11/10
Y1 - 2014/11/10
N2 - We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers under fairly weak conditions on the underlying measure μ. Our main tools are a general concentration inequality for determinantal point processes with a kernel that is a self-adjoint projection, and a strengthening of the Nevai condition from the theory of orthogonal polynomials.
AB - We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers under fairly weak conditions on the underlying measure μ. Our main tools are a general concentration inequality for determinantal point processes with a kernel that is a self-adjoint projection, and a strengthening of the Nevai condition from the theory of orthogonal polynomials.
KW - Concentration inequalities
KW - Determinantal point processes
KW - Local law of large numbers
KW - Nevai condition
KW - Orthogonal polynomial ensembles
KW - Orthogonal polynomials
UR - http://www.scopus.com/inward/record.url?scp=84906739478&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2014.07.026
DO - 10.1016/j.aim.2014.07.026
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AN - SCOPUS:84906739478
SN - 0001-8708
VL - 265
SP - 441
EP - 484
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -