129 citations · 637 across the 37 of their papers we have counts for
7 papers · 1 filter
Algebraic groups in non-commutative probability theory revisited
Ilya Chevyrev, Kurusch Ebrahimi-Fard, Frédéric Patras
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Schürmann. Another algebraic approach…
Gauge field marginal of an Abelian Higgs model
Ajay Chandra, Ilya Chevyrev
We study the gauge field marginal of an Abelian Higgs model with Villain action defined on a 2D lattice in finite volume. Our first main result, which holds for gauge theories on a…
Hopf and pre-Lie algebras in regularity structures
Ilya Chevyrev
These lecture notes aim to present the algebraic theory of regularity structures as developed in arXiv:1303.5113, arXiv:1610.08468, and arXiv:1711.10239. The main aim of this theor…
Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity
Ilya Chevyrev, Tadahiro Oh, Yuzhao Wang
We consider the ill-posedness issue for the cubic nonlinear heat equation and prove norm inflation with infinite loss of regularity in the Hölder-Besov space $\mathcal C^s = B^{s}_…
Norm inflation for a non-linear heat equation with Gaussian initial conditions
Ilya Chevyrev
We consider a non-linear heat equation posed on the -dimensional torus, where is a polynomial of degree at most and is a bilinear…
Stochastic quantisation of Yang-Mills
Ilya Chevyrev
We review two works arXiv:2006.04987 and arXiv:2201.03487 which study the stochastic quantisation equations of Yang-Mills on two and three dimensional Euclidean space with finite v…
Stochastic quantisation of Yang-Mills-Higgs in 3D
Ajay Chandra, Ilya Chevyrev, Martin Hairer +1
We define a state space and a Markov process associated to the stochastic quantisation equation of Yang-Mills-Higgs (YMH) theories. The state space is a nonlinear met…