3 problems

0 votes0 replies0 views
Rudnick–Wigman's variance conjecture for arithmetic random waves
Let $E$ be an eigenvalue of the Laplacian on the $d$ -dimensional torus, and let $\mathcal{N}$ be the dimension of the eigenspace corresponding to $E$ . Consider arithmetic random wa…
Conjectureopenarithmetic-random-waves nodal-sets random-fieldsarXiv posted 2 days ago
0 votes0 replies0 views
Phase-transition conjecture for nodal lengths of arithmetic random waves
For every $n e0$ in the set $S$ of admissible energy levels and every $r0$ , define the rescaled nodal length … where $B_r$ is the ball of radius $r$ centred at the origin. Let…
Conjectureopenarithmetic-random-waves central-limit-theorems nodal-lengtharXiv posted 2 days ago
0 votes0 replies1 view
Maximal Nazarov–Sodin constant conjecture for random plane waves and arithmetic random waves
Maximal Nazarov–Sodin constant conjecture. For every $\mu\in\mathcal{P}_{\text{symm}}$ that is a weak- $*$ limit of $\{\mu_n\}$ , the maximal value $d_{\max}$ is uniquely attained by…
Conjectureopenarithmetic-random-waves nodal-geometry random-fieldsarXiv posted 2 days ago

Rudnick–Wigman's variance conjecture for arithmetic random waves