The motion of a random string

Abstract

We review a series of forthcoming results leading to the construction of a natural evolution on the space of loops with values in a Riemannian manifold. In particular, this clarifies the algebraic structure of the renormalisation procedures appearing in the context of the theory of regularity structures.

Fixed a few typos

References in corpus (3)

• Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\beta$-function, diffeomorphisms and the renormalization group
• An analytic BPHZ theorem for regularity structures
• Algebraic renormalisation of regularity structures

Cited by in corpus (19)

• Renormalising SPDEs in regularity structures
• An analytic BPHZ theorem for regularity structures
• Geometric stochastic heat equations
• A Rough Path Perspective on Renormalization
• A solution theory for quasilinear singular SPDEs
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• Algebraic renormalisation of regularity structures
• Stochastic level-set method for shape optimisation
• Large $N$ limit of the $O(N)$ linear sigma model in 3D
• Some recent progress in singular stochastic PDEs
• Stochastic Ricci Flow on Compact Surfaces
• High order paracontrolled calculus
• An introduction to singular stochastic PDEs: Allen-Cahn equations, metastability and regularity structures
• An Itô type formula for the additive stochastic heat equation
• Continuum limit and preconditioned Langevin sampling of the path integral molecular dynamics
• A tourist's guide to regularity structures and singular stochastic PDEs
• Stochastic Heat Equations for infinite strings with Values in a Manifold
• Stochastic Heat Equations with Values in a Riemannian Manifold
• Spectral gaps for the O-U/Stochastic heat processes on path space over a Riemannian manifold with boundary