学术报告

Completely Monotonic Fredholm Determinants

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题目:Completely Monotonic Fredholm Determinants
报告人:张瑞明 教授 (西北农林科技大学)
地点:致远楼101室
时间:2019年 5月29日 16:00-17:00
摘要: In this talk we discuss some monotonicity questions related to Fredholm matrices and operators. A function $f(x)$ is called completely monotonic if $(-1)^mf^{(m)}(x)>0$. It is known that the expectation of having $m$ eigenvalues of a random Hermitian matrix in an interval is a multiple of $(-1)^{m}$ times the $m$-th derivative of a Fredholm determinant at $\lambda=1$. In this work we extend the positivity to half-real line $(-\infty,1]$, and we also study the completely monotonicity of some special functions which arise as Fredholm determinants.

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