A New Proof of the Abstract Random Tensor Estimate by Deng, Nahmod, and Yue

2025/12/01 by Kaneshiro, Claire
#15B52 #33C45 #35Q55 #60B20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2512.02250

Abstract

We provide a new proof of the abstract random tensor estimate. This estimate was initially proven by Deng, Nahmod, and Yue (2022) using the moment method. The key new tool in our proof is the direct use of the non-commutative Khintchine inequality with the probabilistic decoupling of the product of Gaussians. Hermite and generalized Laguerre-type polynomials allow us to account for pairings in the real and complex-valued Gaussians, respectively, and remove the square-free (tetrahedral) requirement.

Citations

• Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation
• Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics
• Random tensors, propagation of randomness, and nonlinear dispersive equations
• Bounded linear operators between C^*-algebras

Related

• Anticoncentration and Berry--Esseen bounds for random tensors
• Convenient tail bounds for sums of random tensors
• The calculation of expectation values in Gaussian random tensor theory via meanders
• The Hanson-Wright Inequality for Random Tensors
• Generalized Hanson-Wright Inequality for Random Tensors