Zobrazeno 1 - 10
of 106
pro vyhledávání: '"Chevyrev, Ilya"'
Autor:
Chevyrev, Ilya, Mirsajjadi, Hora
We show that any non-linear heat equation with scaling critical dimension $-1$ is locally well-posed when its initial condition is taken as the Gaussian free field in fractional dimension $d < 4$. Our results in particular extend the well-posedness r
Externí odkaz:
http://arxiv.org/abs/2410.11638
In the last decade, the concept of path signature has found great success in data science applications, where it provides features describing the path. This is partly explained by the fact that it is possible to compute the signature of a path in lin
Externí odkaz:
http://arxiv.org/abs/2406.16856
Autor:
Chevyrev, Ilya, Garban, Christophe
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 carpet graph.} This is the lattice gauge theory analog of a well-known prop
Externí odkaz:
http://arxiv.org/abs/2404.09928
Autor:
Chevyrev, Ilya
The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in stochastic analys
Externí odkaz:
http://arxiv.org/abs/2402.10331
We consider deterministic fast-slow dynamical systems of the form \[ x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} A(x_k^{(n)}) + n^{-1/\alpha} B(x_k^{(n)}) v(y_k), \quad y_{k+1} = Ty_k, \] where $\alpha\in(1,2)$ and $x_k^{(n)}\in{\mathbb R}^m$. Here, $T$ is a
Externí odkaz:
http://arxiv.org/abs/2312.15734
We introduce Wilson-It\^o diffusions, a class of random fields on $\mathbb{R}^d$ that change continuously along a scale parameter via a Markovian dynamics with local coefficients. Described via forward-backward stochastic differential equations, thei
Externí odkaz:
http://arxiv.org/abs/2307.11580
Autor:
Chevyrev, Ilya, Shen, Hao
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 associated renormalised Langevin dynamic. Our argument relies on a combinatio
Externí odkaz:
http://arxiv.org/abs/2302.12160
Publikováno v:
Infinite Dimensional Analysis, Quantum Probability and Related Topics 27, No. 03, 2450005 (2024)
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Sch\"urmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie calculus,
Externí odkaz:
http://arxiv.org/abs/2208.02585
Autor:
Chandra, Ajay, Chevyrev, Ilya
Publikováno v:
Communications in Mathematical Physics, vol. 405, no. 143 (2024)
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 arbitrary finite graphs and does not assume that the structure group is
Externí odkaz:
http://arxiv.org/abs/2207.05443
Autor:
Chevyrev, Ilya
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 theory is to build a systematic approach to renormalisation of singular SPD
Externí odkaz:
http://arxiv.org/abs/2206.14557