# Questions tagged [regularity-structures]

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### 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 ...

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### 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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### 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 ...

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

This is related to the paper in the link: https://arxiv.org/abs/1610.08468 titled "Algebraic normalisation of regularity structures". In the method of re-normalization the functional $g$ ...

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### 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 ...

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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 ...

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### Is 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 ...