theory of regularity structures
E926684
The theory of regularity structures is a mathematical framework developed by Martin Hairer to rigorously analyze and solve a broad class of singular stochastic partial differential equations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| theory of regularity structures canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11440064 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: theory of regularity structures Context triple: [Martin Hairer, notableWork, theory of regularity structures]
-
A.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
B.
Malliavin calculus
Malliavin calculus is a branch of stochastic analysis that extends differential calculus to functionals of stochastic processes, particularly Brownian motion, enabling probabilistic proofs of regularity and smoothness for solutions to stochastic differential equations.
-
C.
Bourgain spaces
Bourgain spaces are function spaces introduced by Jean Bourgain that are tailored to study the well-posedness and regularity of nonlinear dispersive partial differential equations.
-
D.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
-
E.
Kolmogorov continuity theorem
The Kolmogorov continuity theorem is a fundamental result in probability theory that provides conditions under which a stochastic process admits a modification with continuous (or Hölder-continuous) sample paths.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: theory of regularity structures Target entity description: The theory of regularity structures is a mathematical framework developed by Martin Hairer to rigorously analyze and solve a broad class of singular stochastic partial differential equations.
-
A.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
B.
Malliavin calculus
Malliavin calculus is a branch of stochastic analysis that extends differential calculus to functionals of stochastic processes, particularly Brownian motion, enabling probabilistic proofs of regularity and smoothness for solutions to stochastic differential equations.
-
C.
Bourgain spaces
Bourgain spaces are function spaces introduced by Jean Bourgain that are tailored to study the well-posedness and regularity of nonlinear dispersive partial differential equations.
-
D.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
-
E.
Kolmogorov continuity theorem
The Kolmogorov continuity theorem is a fundamental result in probability theory that provides conditions under which a stochastic process admits a modification with continuous (or Hölder-continuous) sample paths.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
analytical framework
ⓘ
mathematical theory ⓘ |
| appliesTo |
Φ^4_3 stochastic PDE
ⓘ
KPZ equation NERFINISHED ⓘ a broad class of singular SPDEs ⓘ stochastic heat equation with multiplicative noise ⓘ stochastic quantization equations ⓘ |
| basedOn |
ideas from renormalization in quantum field theory
ⓘ
ideas from rough path theory ⓘ |
| characteristic |
generalizes Taylor expansions to irregular functions and distributions
ⓘ
provides a robust solution theory for highly singular equations ⓘ separates analytic and probabilistic aspects of SPDEs ⓘ uses graded structures of modelled distributions ⓘ |
| contributedTo |
rigorous construction of
Φ^4_3 quantum field models via SPDEs
ⓘ
solution of the KPZ equation in one dimension ⓘ |
| coreConcept |
model
ⓘ
modelled distribution ⓘ reconstruction operator ⓘ regularity structure ⓘ renormalization of models ⓘ structure group ⓘ |
| describedIn | article "A theory of regularity structures" NERFINISHED ⓘ |
| developer | Martin Hairer NERFINISHED ⓘ |
| difficulty | advanced graduate and research-level theory ⓘ |
| field |
mathematical physics
ⓘ
partial differential equations ⓘ probability theory ⓘ stochastic analysis ⓘ stochastic partial differential equations ⓘ |
| impact |
provided a unifying framework for many previously ad hoc renormalization techniques
ⓘ
transformed the study of singular SPDEs ⓘ |
| inspiredBy | Taylor polynomials and jets ⓘ |
| introducedBy | Martin Hairer NERFINISHED ⓘ |
| introducedIn | 2014 ⓘ |
| publishedIn | Inventiones Mathematicae NERFINISHED ⓘ |
| purpose |
construction of solutions to singular SPDEs
ⓘ
renormalization of ill-posed stochastic PDEs ⓘ rigorous analysis of singular stochastic partial differential equations ⓘ |
| recognizedBy | Fields Medal citation of Martin Hairer in 2014 ⓘ |
| relatedTo |
paracontrolled distributions
ⓘ
renormalization group methods ⓘ rough path theory ⓘ |
| usesTool |
Banach space techniques
ⓘ
combinatorial Hopf algebras ⓘ multiscale analysis ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: theory of regularity structures Description of subject: The theory of regularity structures is a mathematical framework developed by Martin Hairer to rigorously analyze and solve a broad class of singular stochastic partial differential equations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.