1 research outputs found
On level line fluctuations of SOS surfaces above a wall
We study the low temperature D Solid-On-Solid model on
with zero boundary conditions and non-negative heights (a floor at height ).
Caputo et al. (2016) established that this random surface typically admits
either or many nested macroscopic level line
loops for an explicit ,
and its top loop has cube-root fluctuations: e.g., if
is the vertical displacement of from the bottom boundary point
, then over . It is believed that rescaling by
and by would yield a limit law of a diffusion on
. However, no nontrivial lower bound was known on for a fixed
(e.g., ), let alone on in , to
complement the bound on . Here we show a lower bound of the
predicted order : for every there exists such
that with probability at least
. The proof relies on the Ornstein--Zernike machinery due to
Campanino--Ioffe--Velenik, and a result of Ioffe, Shlosman and Toninelli (2015)
that rules out pinning in Ising polymers with modified interactions along the
boundary. En route, we refine the latter result into a Brownian excursion limit
law, which may be of independent interest.Comment: 48 pages, 2 figure