Formulae for the derivative of the Poincaré constant of Gibbs measures

Ané, 2000, Sur Les inégalités de Sobolev Logarithmiques, xvi+217 Bakry, 1994, L’hypercontractivité et son utilisation en théorie des semigroupes, vol. 1581, 1 Bakry, 1985, Diffusions hypercontractives, vol. 1123, 177 Bakry, 2014, Analysis and Geometry of Markov Diffusion Operators, xx+552, 10.1007/978-3-319-00227-9_3 Barthe, 2003, Sobolev inequalities for probability measures on the real line, Studia Math., 159, 481, 10.4064/sm159-3-9 Bauerschmidt, 2019, A very simple proof of the LSI for high temperature spin systems, J. Funct. Anal., 276, 2582, 10.1016/j.jfa.2019.01.007 Bobkov, 1999, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal., 163, 1, 10.1006/jfan.1998.3326 Bobkov, 2009, Hardy type inequalities via Riccati and Sturm-Liouville equations, vol. 8, 69 Deuschel, 1989, vol. 137, xiv+307 Dyson, 1978, Phase transitions in quantum spin systems with isotropic and nonisotropic interactions, J. Stat. Phys., 18, 335, 10.1007/BF01106729 Evans, 1998, vol. 19, xviii+662 Gross, 1975, Logarithmic sobolev inequalities, Amer. J. Math., 97, 1061, 10.2307/2373688 Guionnet, 2003, Lectures on logarithmic Sobolev inequalities, vol. 1801, 1 Kato, 1950, On the adiabatic theorem of quantum mechanics, J. Phys. Soc. Japan, 5, 435, 10.1143/JPSJ.5.435 Kato, 1995, xxii+619 Ledoux, 2001, vol. 89, x+181 Lions, 1984, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37, 511, 10.1002/cpa.3160370408 Martinelli, 1999, Lectures on Glauber dynamics for discrete spin models, vol. 1717, 93 Miclo, 2008, Quand est-ce que des bornes de Hardy permettent de calculer une constante de Poincaré exacte sur la droite?, Ann. Fac. Sci. Toulouse Math. (6), 17, 121, 10.5802/afst.1179 Muckenhoupt, 1972, Hardy’s inequality with weights, Studia Math., 44, 31, 10.4064/sm-44-1-31-38 Reed, 1978, xv+396 Rothaus, 1980, Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators, J. Funct. Anal., 39, 42, 10.1016/0022-1236(80)90018-X Rothaus, 1981, Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators, J. Funct. Anal., 42, 110, 10.1016/0022-1236(81)90050-1 Roustant, 2017, Poincaré inequalities on intervals—Application to sensitivity analysis, Electron. J. Stat., 11, 3081, 10.1214/17-EJS1310 Royer, 2007, vol. 14, viii+119 Saloff-Coste, 2002, vol. 289, x+190 Skorokhod, 1961, Stochastic equations for diffusion processes in a bounded region. I, Theory Probab. Appl., 6, 264, 10.1137/1106035 Skorokhod, 1962, Stochastic equations for diffusion processes in a bounded region. II, Theory Probab. Appl., 7, 3, 10.1137/1107002 Stroock, 1971, Diffusion processes with boundary conditions, Comm. Pure Appl. Math., 24, 147, 10.1002/cpa.3160240206