Year: 2026
Type: preprint
Abstract: We prove a dimension-free Markov--Bernstein-type inequality for polynomial mappings $(f_1,f_2)\colon\mathbb R^n\to\mathbb R^2$ of degree at most $d$. For product probability measures whose one-dimensional marginals have densities bounded by $1$, we obtain a lower bound for the integral of the Gram determinant of $\nabla f_1$ and $\nabla f_2$ in terms of the Gram determinant of the $d$-th derivative tensors $D^df_1$ and $D^df_2$, with a constant depending only on $d$. For pairs in a fixed Wiener chaos, the resulting Gaussian inequality answers a question of Nourdin, Nualart, and Poly concerning a lower bound for the expectation of the Malliavin determinant in terms of the determinant of the covariance matrix.
Source: arXiv (Cornell University)
Author: Kosov, Egor
Institution: Centre de Recerca Matemàtica
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221531757