Page 569 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 569
STOCHASTIC EVOLUTION EQUATIONS (MS-68)
High-frequency analysis for parabolic stochastic PDEs
Carsten Chong, carsten.chong@epfl.ch
EPFL - Swiss Federal Institute of Technology Lausanne, Switzerland
We consider the stochastic heat equation driven by an additive or multiplicative Gaussian noise
that is white in time and spatially homogeneous in space. Assuming that the spatial correlation
function is given by a Riesz kernel of order α ∈ (0, 2 ∧ d), where d is the spatial dimension, we
prove a central limit theorem for the power variations of the solution in the additive case. We
further show that the same central limit theorem is valid with multiplicative noise if α ∈ (0, 1)
but fails in general if α = 1 (and d ≥ 2) or if the noise is a space-time white noise (and d = 1).
If time permits, we discuss applications of our results to statistical estimation for the stochastic
heat equation.
Stochastic quantization of exponential-type quantum field theories
Francesco Carlo De Vecchi, francesco.devecchi@uni-bonn.de
Universität Bonn, Germany
Stochastic quantization is a method, proposed by Parisi and Wu, of constructive Euclidean quan-
tum field theory for building the Schwinger functions of a quantum model from the invariant
solutions of suitable (parabolic, hyperbolic or elliptic) stochastic partial differential equations
(SPDEs). In the talk we provide an introduction to the topic and to the recent developments
in the field, focusing on the analytic and probabilistic aspects of the problem. We propose a
more detailed analysis of the SPDEs related to the two-dimensional exponential-type models
such as the Høegh-Krohn, or Liouville quantum gravity, quantum field theory and the massive
sinh(ϕ)2 interaction. The talk is mainly based on the joint work [1] with Sergio Albeverio and
Massimiliano Gubinelli, and a paper in preparation with Nikolay Barashkov.
References
[1] Albeverio, Sergio, Francesco C. De Vecchi, and Massimiliano Gubinelli. “The ellip-
tic stochastic quantization of some two dimensional Euclidean QFTs." arXiv preprint
arXiv:1906.11187, to appear in Annales de l’Institut Henri Poincaré.
Non-equilibrium fluctuations in interacting particle systems and
conservative stochastic PDE
Benjamin Fehrman, fehrman@maths.ox.ac.uk
University of Oxford, United Kingdom
Coauthor: Benjamin Gess
Interacting particle systems have found diverse applications in mathematics and several related
fields, including statistical physics, population dynamics, and machine learning. We will fo-
cus, in particular, on the zero range process and the symmetric simple exclusion process. The
large-scale behavior of these systems is essentially deterministic, and is described in terms of a
hydrodynamic limit. However, the particle process does exhibit large fluctuations away from its
567
High-frequency analysis for parabolic stochastic PDEs
Carsten Chong, carsten.chong@epfl.ch
EPFL - Swiss Federal Institute of Technology Lausanne, Switzerland
We consider the stochastic heat equation driven by an additive or multiplicative Gaussian noise
that is white in time and spatially homogeneous in space. Assuming that the spatial correlation
function is given by a Riesz kernel of order α ∈ (0, 2 ∧ d), where d is the spatial dimension, we
prove a central limit theorem for the power variations of the solution in the additive case. We
further show that the same central limit theorem is valid with multiplicative noise if α ∈ (0, 1)
but fails in general if α = 1 (and d ≥ 2) or if the noise is a space-time white noise (and d = 1).
If time permits, we discuss applications of our results to statistical estimation for the stochastic
heat equation.
Stochastic quantization of exponential-type quantum field theories
Francesco Carlo De Vecchi, francesco.devecchi@uni-bonn.de
Universität Bonn, Germany
Stochastic quantization is a method, proposed by Parisi and Wu, of constructive Euclidean quan-
tum field theory for building the Schwinger functions of a quantum model from the invariant
solutions of suitable (parabolic, hyperbolic or elliptic) stochastic partial differential equations
(SPDEs). In the talk we provide an introduction to the topic and to the recent developments
in the field, focusing on the analytic and probabilistic aspects of the problem. We propose a
more detailed analysis of the SPDEs related to the two-dimensional exponential-type models
such as the Høegh-Krohn, or Liouville quantum gravity, quantum field theory and the massive
sinh(ϕ)2 interaction. The talk is mainly based on the joint work [1] with Sergio Albeverio and
Massimiliano Gubinelli, and a paper in preparation with Nikolay Barashkov.
References
[1] Albeverio, Sergio, Francesco C. De Vecchi, and Massimiliano Gubinelli. “The ellip-
tic stochastic quantization of some two dimensional Euclidean QFTs." arXiv preprint
arXiv:1906.11187, to appear in Annales de l’Institut Henri Poincaré.
Non-equilibrium fluctuations in interacting particle systems and
conservative stochastic PDE
Benjamin Fehrman, fehrman@maths.ox.ac.uk
University of Oxford, United Kingdom
Coauthor: Benjamin Gess
Interacting particle systems have found diverse applications in mathematics and several related
fields, including statistical physics, population dynamics, and machine learning. We will fo-
cus, in particular, on the zero range process and the symmetric simple exclusion process. The
large-scale behavior of these systems is essentially deterministic, and is described in terms of a
hydrodynamic limit. However, the particle process does exhibit large fluctuations away from its
567
