The ordered elements in several one-dimensional Coulomb gas ensembles arising in probability and mathematical physics are shown to have log- concave distributions. Examples include the beta ensembles with convex potentials (in the continuous setting) and the orthogonal polynomial ensembles (in the discrete setting). In particular, we prove the log-concavity of the Tracy-Widom β distributions, Airy distribution, Airy-2 process. Log-concavity of last passage times in percolation is proven using their connection to Meixner ensembles. As a result we prove the log-concavity of top rows of Young diagrams under Poissonized Plancherel measure, which is Poissonized version of a conjecture of Chen.
This is ongoing joint work with Manjunath Krishnapur and Mokshay Madiman.
Zoom link: https://us02web.zoom.us/j/88670406480
Meeting ID: 886 7040 6480
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