主 题: Maxima of two-dimensional discrete Gaussian free field
报告人: Dr. Ding Jian (Univ. of Chicago, USA)
时 间: 2012-09-03 15:00-16:00
地 点: 理科一号楼 1418
In this talk, I will present progresses on the maximum/maxima of the
2D discrete Gaussian free field. On one hand, we have now developed
good understanding on the single maximum due to efforts over more than
a decade. I will survey a line of works which established its
asymptotics and fluctuation, as well as the tail behavior.
Nevertheless, the limiting law of the centered maximum remains a
challenge at the moment. On the other hand, our understanding for the
joint behavior of the maxima is still preliminary, compared to the
analogous picture obtained for Branching Brownian motion. I will
report a recent work (with Ofer Zeitouni) along this direction, which
particularly shows that the particles of large values are either close
or far away from each other. The question on the scaling limit of the
maxima remains open.
The talk is based on works by Bramson, Bolthausen, Chatterjee,
