Complexity of Gaussian Random Fields with Isotropic Increments

We study the energy landscape of a model single particle on random potential, that is, we investigate topology level sets smooth fields $${\mathbb {R}}^{N}$$ form $$X_N(x) +\frac{\mu }{2} \Vert x\Vert ^2,$$ where $$X_{N}$$ is Gaussian process with isotropic increments. derive asymptotic formulas for mean number critical points values in an open set as dimension N goes to infinity. In companion paper, provide same analysis given index.