Staying positive: bounds for non-Gaussian noise in Schwinger-Keldysh effective field theory

@misc{amoretti2026staying,
  title = {{Staying positive: bounds for non-Gaussian noise in Schwinger-Keldysh effective field theory}},
  author = {Andrea Amoretti and Daniel K. Brattan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12050},
  eprint = {2609.12050},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12050},
}

TY  - UNPB
TI  - Staying positive: bounds for non-Gaussian noise in Schwinger-Keldysh effective field theory
AU  - Andrea Amoretti
AU  - Daniel K. Brattan
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.12050
UR  - https://arxiv.org/abs/2609.12050
AB  - Modern effective field theories of dissipative hydrodynamics, built on the Schwinger-Keldysh (SK) formalism, include thermal noise that is not Gaussian. The resultant higher-order noise vertices are constrained by symmetries, but otherwise treated as free parameters. We show explicitly that symmetry constraints alone do not guarantee these vertices yield a genuine probability distribution. Requiring a probability interpretation yields sharp bounds between cumulants that are invisible to the symmetry analysis. The bounds are optimal: their boundaries are attained by explicit positive distributions, and constructive completions are provided for both negative- and positive-kurtosis noise data. This gives closed-form nonlinear response and an exact sampling algorithm, whose Monte Carlo implementation reproduces the exact cumulants and nonlinear fluctuation-dissipation relations. Confronted with microscopic results, the framework places a sharp lower bound on the time step required for a positive stochastic completion of a quartic model of the Brownian particle used in the literature, while holographically computed SU(2) noise vertices pass a nontrivial continuum fourth-order positivity test.
ER  -