Riemann surfaces上随机解析函数固定Morse指标的临界值
Critical values of fixed Morse index of random analytic functions on Riemann surfaces
摘要：
本注记是“复流形上随机解析函数的临界值”的附录，印第安纳大学数学杂志63第3期（2014年），第651-686页。作者R.Feng和S. Zelditch（arXiv：1212.4762）.本文给出了Morse指数固定的随机解析函数临界点处临界值的极限分布公式，并在Riemann曲面的情况下，显式地计算了局部极大值和鞍值的极限，证明了临界值分布的完全展开式中的二阶项在Riemann曲面上是拓扑不变的.
英文摘要：
This note is an addendum to 'Critical values of random analytic functions on complex manifolds, Indiana Univ. Math. J. 63 No. 3 (2014), 651-686.' by R.Feng and S. Zelditch (arXiv:1212.4762). In this note, we give the formula of the limiting distribution of the critical values at critical points of random analytic functions of fixed Morse index and we compute explicitly such limitings for local maxima and saddle values in the case of Riemann surfaces; we also prove that the second order term in the full expansion of the distribution of the critical values is topologically invariant on Riemann surfaces.
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