Statistics of Stationary Points of Random Finite Polynomial Potentials

Understand

The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and Mathematical Biology.

• However, there are few reliable methods available which can find all the SPs accurately.
• Hence, one has to rely on indirect methods such as Random Matrix theory.
• With a combination of the numerical polynomial homotopy continuation method and a certification method, we obtain all the certified SPs of the most general polynomial RP for each sample chosen from the Gaussian distribution with mean 0 and variance 1.