$\mathrm{GL}(n,{\mathbb{Z}}_p)$-invariant Gaussian measures on the space of $p$-adic polynomials

Yassine EL Maazouz, Antonio Lerario

We prove that if $p>d$ there is a unique gaussian distribution (in the sense of Evans) on the space ${\mathbb{Q}}_p[x_1,\dots ,x_n{]}_{(d)}$ which is invariant under the action of $\…