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This introduction surveys a renormalisation group perspective on log-Sobolev inequalities and related properties of stochastic dynamics.
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École d’été de probabilités de Saint-Flour XV-XVII, 1985-87 (2-19 Juil. 1985, 17 Août - 3 Sept. 1986, 1-18 Juil. 1987)
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G. Royer · 1999
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The log-Sobolev inequality for weakly coupled lattice fields
N. Yoshida · 1999
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Sine-Gordon revisited
J. Dimock and T.R. Hurd · 2000
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The concentration of measure phenomenon
M. Ledoux · 2001
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On Extensions of the Brunn-Minkowski and Prékopa-Leindler Theorems, Including Inequalities for Log Concave Functions, and with an Application to the Diffusion Equation
H.J. Brascamp and E.H. Lieb · 2002
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A. Guionnet and B. Zegarlinski · 2003
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Relaxation times of Markov chains in statistical mechanics and combinatorial structures
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Modified logarithmic Sobolev inequalities in discrete settings
S.G. Bobkov and P. Tetali · 2006
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Hamilton’s Ricci flow
B. Chow, P. Lu, and L. Ni · 2006
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Controlled Markov processes and viscosity solutions
W.H. Fleming and H.M. Soner · 2006
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Counting independent sets up to the tree threshold
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Perspectives in statistical mechanics
M. Aizenman · 2007
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Optimal transport and Perelman’s reduced volume
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Uniform logarithmic Sobolev inequality for Boltzmann measures with exterior magnetic field over spheres
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A generalization of Caffarelli’s contraction theorem via (reverse) heat flow
Y.-H. Kim and E. Milman · 2012
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Cutoff for the Ising model on the lattice
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The Φ 3 4 \Phi^{4}_{3} measure via Girsanov’s theorem
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Log-Sobolev inequality for the continuum sine-Gordon model
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Analysis of high-dimensional distributions using pathwise methods
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Spectral monotonicity under Gaussian convolution
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