TY - JOUR
AB - We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion.
AU - Cipolloni, Giorgio
AU - Erdös, László
AU - Xu, Yuanyuan
ID - 17375
IS - 6
JF - Journal of Mathematical Physics
SN - 0022-2488
TI - Precise asymptotics for the spectral radius of a large random matrix
VL - 65
ER -