Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A path property of Dyson gaps, Plancherel measures for $Sp(\infty)$, and
  random surface growth   We pursue applications for symplectic Plancherel growth based on a repulsion
phenomenon arising in its diffusion limit and on intermediate representation
theory underlying its correlation structure. Under diffusive scaling, the
dynamics converge to interlaced reflecting Brownian motions with a wall that
achieve Dyson non-colliding dynamics. We exhibit non-degeneracy of constraint
in this coupled system by deriving a path property that quantifies repulsion
between particles coinciding in the limit. We then identify consistent series
of Plancherel measures for $Sp(\infty)$ that reflect the odd symplectic groups,
despite their non-semisimplicity. As an application, we compute the correlation
kernel of the growth model and investigate its local asymptotics: the
incomplete beta kernel emerges in the bulk limit, and new variants of the
Jacobi and Pearcey kernels arise as edge limits. In particular, we provide
further evidence for the universality of the $1/4$-growth exponent and Pearcey
point process in the class of anisotropic KPZ with a wall.

3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an