Universality of the nodal length of bivariate random trigonometric polynomials

@article{Angst2018UniversalityOT,
  title={Universality of the nodal length of bivariate random trigonometric polynomials},
  author={Jurgen Angst and Guillaume Poly and Hung Pham Viet},
  journal={Transactions of the American Mathematical Society},
  year={2018}
}
We consider random trigonometric polynomials of the form \[ f_n(x,y)=\sum_{1\le k,l \le n} a_{k,l} \cos(kx) \cos(ly), \] where the entries $(a_{k,l})_{k,l\ge 1}$ are i.i.d. random variables that are centered with unit variance. We investigate the length $\ell_K(f_n)$ of the nodal set $Z_K(f_n)$ of the zeros of $f_n$ that belong to a compact set $K \subset \mathbb R^2$. We first establish a local universality result, namely we prove that, as $n$ goes to infinity, the sequence of random variables… 

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