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What are morphisms between regularity structures?
In Hairer's notes A Theory of Regularity Structures he defines automorphisms of a regularity structure on page 28. I will recall the definition here:Is there any way of extending this to morphisms...
View ArticleIs there any reason to use paracontrolled calculus over regularity structures?
Paracontrolled calculus was developed by Gubinelli, Imkeller and Perkowski as a way of treating singular stochastic PDEs such as KPZ, $\Phi_3^4$ or PAM, around the same time regularity structures were...
View ArticleHow to compare pathwise convergence and convergence in probability
This question was asked quite sometime back in mathexchange and deleted, as it was downvoted, asked again but never got an answer. So I am asking here.Motivation: It appears pathwise convergence can...
View ArticleWhen and why do we require the condition that :"a subset bounded from below...
I have been tyring to understand the first condition given in the link https://en.wikipedia.org/wiki/Regularity_structure for quite some time now, at least a year. I have posted a similar question in...
View ArticleWhy does the correct scaled dimension for SPDEs count time as two dimensions?
In this video, Felix Otto says that the correct way to count dimensions for parabolic equations is $2+\text{number of space dimensions}$. He said nothing about this. In the accompanying notes it is...
View ArticleCan we extend regularity structure to matrix?
I have been trying to understand if we can apply regularity structure to solve differential equations related to Gorini–Kossakowski–Sudarshan–Lindblad or GKSL equations. This is also known as the...
View ArticleRough paths, unparametrized path space, and Kontsevich's moduli space of...
Let $X$ be a manifold. Modulo reparametrization, the path space of $X$ is a groupoid $\Pi_X$. In Kapranov's "Free Lie Algebroids and the Space of Paths", Kapranov constructs an associated Lie algebroid...
View ArticleDo regularity structures involve infinite "Taylor" series?
I have been learning about the theory of regularity structures, for which the common motivation is Taylor series. However, I keep seeing direct sums in the definition of a regularity structure, which...
View ArticleAlgebraic normalisation of regularity structures: can there be a explicit...
This is related to Bruned, Hairer, and Zambotti - Algebraic renormalisation of regularity structures. In the method of re-normalization the functional $g$ shown in page 6 plays a major role. However,...
View ArticleTruncated fixed point and regularity structures
This question arose via the helpful comments on this earlier question.In Hairer's theory of regularity structures, fixed point problems are first solved in certain spaces $D^\gamma$ which consist of...
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