## Rocky Mountain Journal of Mathematics

### Lower bounds for the Estrada index using mixing time and Laplacian spectrum

Yilun Shang

#### Abstract

The logarithm of the Estrada index has been recently proposed as a spectral measure to characterize the robustness of complex networks. We derive novel analytic lower bounds for the logarithm of the Estrada index based on the Laplacian spectrum and the mixing times of random walks on the network. The main techniques employed are some inequalities, such as the thermodynamic inequality in statistical mechanics, a trace inequality of von Neumann, and a refined harmonic-arithmetic mean inequality.

#### Article information

Source
Rocky Mountain J. Math., Volume 43, Number 6 (2013), 2009-2016.

Dates
First available in Project Euclid: 25 February 2014

https://projecteuclid.org/euclid.rmjm/1393336666

Digital Object Identifier
doi:10.1216/RMJ-2013-43-6-2009

Mathematical Reviews number (MathSciNet)
MR3178453

Zentralblatt MATH identifier
1345.05042

#### Citation

Shang, Yilun. Lower bounds for the Estrada index using mixing time and Laplacian spectrum. Rocky Mountain J. Math. 43 (2013), no. 6, 2009--2016. doi:10.1216/RMJ-2013-43-6-2009. https://projecteuclid.org/euclid.rmjm/1393336666

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