Questions tagged [regularity-structures]

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Truncated 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 ...
• 407
236 views

Do 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 ...
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70 views

Can 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 ...
• 475
349 views

Rough paths, unparametrized path space, and Kontsevich's moduli space of stable maps

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 ...
579 views

How 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 ...
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198 views

When and why do we require the condition that :"a subset bounded from below and has no accumulation points?"

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 ...
• 475
198 views

Algebraic normalisation of regularity structures: can there be a explicit expression of g?

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, ...
202 views

Why 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 ...
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 ...