4 papers
Asymptotic expansion of the hard-to-soft edge transition
Luming Yao, Lun Zhang
By showing that the symmetrically transformed Bessel kernel admits a full asymptotic expansion for large parameter, we establish a hard-to-soft edge transition expansion. This reso…
Asymptotics for the noncommutative Painlevé II equation
Junwen Liu, Luming Yao, Lun Zhang
In this paper, we are concerned with the following noncommutative Painlevé II equation \begin{equation*} \mathbf{D}^2 β_1 = 4\mathbf{s} β_1 +4 β_1 \mathbf{s} +8 β_1^3, \end{eq…
The multiplicative constant in asymptotics of higher-order analogues of the Tracy-Widom distribution
Dan Dai, Wen-Gao Long, Shuai-Xia Xu +2
In this paper, we are concerned with higher-order analogues of the Tracy-Widom distribution, which describe the eigenvalue distributions in unitary random matrix models near critic…
Large gap asymptotics of the hard edge tacnode process
Junwen Liu, Luming Yao, Lun Zhang
A special type of geometric situation in ensembles of non-intersecting paths occurs when the non-intersecting trajectories are required to be nonnegative so that the limit shape be…