The Poincaré constant 
of a probability
measure on 
is the least constant for which
 |
for every sufficiently regular function 
, where 
is its variance.
This is the Poincaré inequality for
.
The Kannan-Lovász-Simonovits conjecture asserts a universal upper bound on 
for isotropic logarithmically
concave distributions. Bizeul et al. (2026) reported a proof of this bound.
Balasubramanian and Kasiviswanathan (2026) reported a deterministic variational proof of the explicit bound 
for every isotropic logarithmically concave distribution 
, independently of dimension.
Balasubramanian and Kasiviswanathan (2026) acknowledge AI assistance and take responsibility
for the content. The complete argument has not been independently verified here.
