Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random tensors, propagation of randomness, and nonlinear dispersive
  equations   Abstract. The purpose of this paper is twofold. We introduce the theory of
random tensors, which naturally extends the method of random averaging
operators in our earlier work arXiv:1910.08492, to study the propagation of
randomness under nonlinear dispersive equations. By applying this theory we
also solve Conjecture 1.7 in arXiv:1910.08492, and establish almost-sure local
well-posedness for semilinear Schr\"{o}dinger equations in spaces that are
subcritical in the probabilistic scaling. The solution we find has an explicit
expansion in terms of multilinear Gaussians with adapted random tensor
coefficients.
  In the random setting, the probabilistic scaling is the natural scaling for
dispersive equations, and is different from the natural scaling for parabolic
equations. Our theory, which covers the full subcritical regime in the
probabilistic scaling, can be viewed as the dispersive counterpart of the
existing parabolic theories (regularity structure, para-controlled calculus and
renormalization group techniques).

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex