11 papers
Invariant measure and universality of the 2D Yang-Mills Langevin dynamic
Ilya Chevyrev, Hao Shen
We prove that the Yang-Mills (YM) measure for the trivial principal bundle over the two-dimensional torus, with any connected, compact structure group, is invariant for the associa…
Orthogonal polynomials on path-space
Ilya Chevyrev, Emilio Ferrucci, Darrick Lee +3
We consider the orthogonalisation of the signature of a stochastic process as the analogue of orthogonal polynomials on path-space. Under an infinite radius of convergence assumpti…
Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs
Ilya Chevyrev, Hao Shen
Local solutions to the 3D stochastic quantisation equations of Yang-Mills-Higgs were constructed in (arXiv:2201.03487), and it was shown that, in the limit of smooth mollifications…
Local well-posedness of subcritical non-linear heat equations with Gaussian initial data
Ilya Chevyrev, Hora Mirsajjadi
We show that any non-linear heat equation with scaling critical dimension is locally well-posed when its initial condition is taken as the Gaussian free field in fractional di…
Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime
Ajay Chandra, Ilya Chevyrev
We propose an elementary method to show non-Gaussianity of invariant measures of parabolic stochastic partial differential equations with polynomial non-linearities in the Da Prato…
Villain action in lattice gauge theory
Ilya Chevyrev, Christophe Garban
We prove that Villain interaction applied to lattice gauge theory can be obtained as the limit of both Wilson and Manton interactions on a larger graph which we call the {\em carpe…