TY - JOUR
T1 - EXPONENTIAL OF THE S1 TRACE OF THE FREE FIELD AND VERBLUNSKY COEFFICIENTS
AU - Latifi, Mohammad Javad
AU - Pickrell, Doug
N1 - Publisher Copyright: © 2022 Rocky Mountain Mathematics Consortium. All rights reserved.
PY - 2022/6
Y1 - 2022/6
N2 - An identity of Szego, and a volume calculation, heuristically suggest a simple expression for the distribution of Verblunsky coefficients with respect to the (normalized) exponential of the S1 trace of the Gaussian free field. This heuristic expression is not quite correct. A proof of the correct formula has been found by Chhaibi and Najnudel (2019). Their proof uses random matrix theory and overcomes many difficult technical issues. In addition to presenting the Szego perspective, we show that the Chhaibi and Najnudel theorem implies a family of combinatorial identities (for moments of measures) which are of intrinsic interest.
AB - An identity of Szego, and a volume calculation, heuristically suggest a simple expression for the distribution of Verblunsky coefficients with respect to the (normalized) exponential of the S1 trace of the Gaussian free field. This heuristic expression is not quite correct. A proof of the correct formula has been found by Chhaibi and Najnudel (2019). Their proof uses random matrix theory and overcomes many difficult technical issues. In addition to presenting the Szego perspective, we show that the Chhaibi and Najnudel theorem implies a family of combinatorial identities (for moments of measures) which are of intrinsic interest.
KW - Gaussian free field
KW - Loop group factorization
KW - Verblunsky coefficients
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U2 - 10.1216/rmj.2022.52.899
DO - 10.1216/rmj.2022.52.899
M3 - Article
SN - 0035-7596
VL - 52
SP - 899
EP - 924
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 3
ER -