Abstract
The main topic of this talk is the speed estimation of stability/instability. The word “various” comes with no surprising since there are a lot of different types of stability/instability and each of them has its own natural distance to measure. However, the adjective “unified” is very much unexpected. The talk surveys our recent progress on the topic, made in the past five years or so.
References
[1] Chen, M.F. (2003). Variational formulas of Poincaré-type inequalities for birth-death processes. Acta Math. Sin. Eng. Ser. 19(4): 625-644.Search in Google Scholar
[2] Chen, M.F. (2004). From Markov Chains to Non-equilibrium Particle Systems. World Scientific. 2nd ed. (1st ed., 1992).10.1142/5513Search in Google Scholar
[3] Chen, M.F. (2005). Eigenvalues, Inequalities, and Ergodic Theory. Springer, London.Search in Google Scholar
[4] Chen, M.F. (2007). Exponential convergence rate in entropy. Front. Math. China, 2(3): 329–358.Search in Google Scholar
[5] Chen M.F. (2010). Speed of stability for birth–death processes. Front Math China 5(3): 379–515.Search in Google Scholar
[6] Chen, M.F. (2012). Lower bounds of principal eigenvalue in dimension one. Front. Math. China 7(4): 645–668.Search in Google Scholar
[7] Chen, M.F. (2013a). Bilateral Hardy-type inequalities. Acta Math Sin Eng Ser. 29(1): 1–32.10.1007/s10114-012-2316-0Search in Google Scholar
[8] Chen, M.F. (2013b). Bilateral Hardy-type inequalities and application to geometry. Mathmedia 37(2): 12–32; Math. Bulletin 52(8/9) (in Chinese).Search in Google Scholar
[9] Chen, M.F. (2014). Criteria for discrete spectrum of 1D operators. Commu. Math. Stat. 2: 279–30910.1007/s40304-014-0041-ySearch in Google Scholar
[10] Chen, M.F. (2015a). Criteria for two spectral problems of 1D operators (in Chinese). Sci Sin Math, 44(1):10.1360/N012014-00282Search in Google Scholar
[11] Chen, M.F. (2015b). The optimal constant in Hardy-type inequalities. Acta Math. Sinica, Eng. Ser.10.1007/s10114-015-4731-5Search in Google Scholar
[12] Chen, M.F. (2015c). Progress on Hardy-type inequalities. Chapter 6 in the book “Festschrift Masatoshi Fukushima”, eds: Z.Q. Chen, N. Jacob, M. Takeda, and T. Uemura, World Sci.10.1142/9789814596534_0007Search in Google Scholar
[13] Chen, M.F. and Zhang, X. (2014) Isospectral operators. Commu Math Stat 2: 17–32.10.1007/s40304-014-0028-8Search in Google Scholar
[14] Liao, Z.W. (2015). Discrete weighted Hardy inequalities with different boundary conditions. arXiv:1508.04601.Search in Google Scholar
© 2016 Mu-Fa Chen, published by De Gruyter Open
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