  Recently the first author and Jang Soo Kim introduced lecture hall tableaux
in their study of multivariate little q-Jacobi polynomials. They then
enumerated bounded lecture hall tableaux and showed that their enumeration is
closely related to standard and semistandard Young tableaux. In this paper we
study the asymptotic behavior of these bounded tableaux thanks to two other
combinatorial models: non intersecting paths on a graph whose faces are squares
and pentagons and dimer models on a lattice whose faces are hexagons and
octogons. We use the tangent method to investigate the arctic curve in the
model of nonintersecting lattice paths with fixed starting points and ending
points distributibuted according to some arbitrary piecewise differentiable
function. We then study the dimer model and use some ansatz to guess the
asymptotics of the inverse of the Kasteleyn matrix confirm the arctic curve
computed with the tangent method for two examples.
