The invariant measure and the flow associated to the -quantum field model
S Albeverio, S Kusuoka - arXiv preprint arXiv:1711.07108, 2017 - arxiv.org
We give a direct construction of invariant measures and global flows for the stochastic
quantization equation to the quantum field theoretical $\Phi^ 4_3 $-model on the $3 …
quantization equation to the quantum field theoretical $\Phi^ 4_3 $-model on the $3 …
The infinitesimal generator of the stochastic Burgers equation
M Gubinelli, N Perkowski - Probability Theory and Related Fields, 2020 - Springer
We develop a martingale approach for a class of singular stochastic PDEs of Burgers type
(including fractional and multi-component Burgers equations) by constructing a domain for …
(including fractional and multi-component Burgers equations) by constructing a domain for …
Log‐Sobolev inequality for the φ 2 4 φ^4_2 and φ 3 4 φ^4_3 measures
R Bauerschmidt, B Dagallier - Communications on Pure and …, 2024 - Wiley Online Library
Abstract The continuum φ 2 4 φ^4_2 and φ 3 4 φ^4_3 measures are shown to satisfy a log‐
Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that …
Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that …
Phase Transitions for
We establish a surface order large deviation estimate for the magnetisation of low
temperature ϕ 3 4. As a byproduct, we obtain a decay of spectral gap for its Glauber …
temperature ϕ 3 4. As a byproduct, we obtain a decay of spectral gap for its Glauber …
Log-Sobolev inequality for the and measures
R Bauerschmidt, B Dagallier - arXiv preprint arXiv:2202.02295, 2022 - arxiv.org
The continuum $\varphi^ 4_2 $ and $\varphi^ 4_3 $ measures are shown to satisfy a log-
Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that …
Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that …
Stochastic Ricci flow on compact surfaces
J Dubédat, H Shen - International Mathematics Research …, 2022 - academic.oup.com
In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow
is symmetric with respect to a measure induced by Liouville conformal field theory. Using the …
is symmetric with respect to a measure induced by Liouville conformal field theory. Using the …
A panorama of singular SPDEs
M Gubinelli - Proceedings of the International Congress of …, 2018 - World Scientific
I will review the setting and some of the recent results in the field of singular stochastic
partial differential equations (SSPDEs). Since Hairer's invention of regularity structures this …
partial differential equations (SSPDEs). Since Hairer's invention of regularity structures this …
Existence of densities for the dynamic model
P Gassiat, C Labbé - 2020 - projecteuclid.org
We apply Malliavin calculus to the Φ^4_3 equation on the torus and prove existence of
densities for the solution of the equation evaluated at regular enough test functions. We work …
densities for the solution of the equation evaluated at regular enough test functions. We work …
Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit
D Luo, R Zhu - Stochastic Processes and their Applications, 2021 - Elsevier
We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D torus T 2,
perturbed by multiplicative transport noise. The equation admits the white noise measure on …
perturbed by multiplicative transport noise. The equation admits the white noise measure on …
Stochastic quantization of the three-dimensional polymer measure via the Dirichlet form method
S Albeverio, S Kusuoka, S Liang… - arXiv preprint arXiv …, 2023 - arxiv.org
We prove that there exists a diffusion process whose invariant measure is the three
dimensional polymer measure $\nu_\lambda $ for small $\lambda> 0$. We follow in part a …
dimensional polymer measure $\nu_\lambda $ for small $\lambda> 0$. We follow in part a …