A Homotopical Geometry of the Multinomial and Negative-Multinomial Potentials

Shintaro Yoshizawa

We study the one-parameter family of Hessian metrics $g_{\alpha }=\alpha h_{+}+(1-\alpha )h_{-}$, $\alpha \in [0,1]$, formed by convexly combining the log-partition functions (not the densities) of the multinomi…