TY - JOUR
T1 - Local Universality for Zeros and Critical Points of Monochromatic Random Waves
AU - Canzani, Yaiza
AU - Hanin, Boris
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - This paper concerns the asymptotic behavior of zeros and critical points for monochromatic random waves ϕλ of frequency λ on a compact, smooth, Riemannian manifold (M, g) as λ→ ∞. We prove global variance estimates for the measures of integration over the zeros and critical points of ϕλ. These global estimates hold for a wide class of manifolds—for example when (M, g) has no conjugate points—and rely on new local variance estimates on zeros and critical points of ϕλ in balls of radius ≈ λ- 1 around a fixed point. Our local results hold under conditions about the structure of geodesics that are generic in the space of all metrics on M.
AB - This paper concerns the asymptotic behavior of zeros and critical points for monochromatic random waves ϕλ of frequency λ on a compact, smooth, Riemannian manifold (M, g) as λ→ ∞. We prove global variance estimates for the measures of integration over the zeros and critical points of ϕλ. These global estimates hold for a wide class of manifolds—for example when (M, g) has no conjugate points—and rely on new local variance estimates on zeros and critical points of ϕλ in balls of radius ≈ λ- 1 around a fixed point. Our local results hold under conditions about the structure of geodesics that are generic in the space of all metrics on M.
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U2 - 10.1007/s00220-020-03826-w
DO - 10.1007/s00220-020-03826-w
M3 - Article
AN - SCOPUS:85089356158
SN - 0010-3616
VL - 378
SP - 1677
EP - 1712
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 3
ER -