Myeongjin Kang

A conditional power stability estimate for the logarithmic Brunn-Minkowski inequality

Assuming the smooth variance and moment-coordinate identities specified in this paper, we prove a power stability estimate for the logarithmic Brunn-Minkowski inequality on origin-symmetric convex bodies. In each dimension at least three, a small deficit forces the two bodies clo...

Dimension- and label-uniform stability of Gaussian propellers

Assume the sharp finite Gaussian propeller inequality and its finite equality classification. We prove that the deficit in the squared first-moment functional controls the square of the Gaussian measure distance to a propeller, with one positive constant independent of the ambien...

A rooted entropy bound for perfect matchings

Let H_G(x) be the maximum entropy of a perfect-matching law with prescribed edge marginals x in a finite loopless multigraph. We prove that, for every vertex v, H_G(x) is at least -sum_e x_e log x_e + (3/2) sum_{e not incident to v} (1-x_e) log(1-x_e). On 2m vertices this gives a...