Related papers: Classifying conformally invariant loop measures
In 1986, Zamolodchikov conjectured an exponential structure for the semi-classical limit of conformal blocks on a sphere. This paper provides a rigorous proof of the analog of Zamolodchikov conjecture for Liouville conformal blocks on a…
We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…
How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with…
We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions and we show that…
The Ghahramani-Lau conjecture is established; in other words, the measure algebra of every locally compact group is strongly Arens irregular. To this end, we introduce and study certain new classes of measures (called approximately…
We find sufficient conditions for a probability measure $\mu$ to satisfy an inequality of the type $$ \int_{\R^d} f^2 F\Bigl(\frac{f^2}{\int_{\R^d} f^2 d \mu} \Bigr) d \mu \le C \int_{\R^d} f^2 c^{*}\Bigl(\frac{|\nabla f|}{|f|} \Bigr) d \mu…
We cast Kasparov's equivariant KK-theory in the framework of model categories. We obtain a stable model structure on a certain category of locally multiplicative convex $G$-$C^*$-algebras, which naturally contains the stable…
We consider Glauber-type stochastic dynamics of continuous systems \cite{BCC02}, \cite{KL03}, a particular case of spatial birth-and-death processes. The dynamics is defined by a Markov generator in such a way that Gibbs measures of Ruelle…
The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects…
A manifestly gauge invariant and regularized renormalization group flow equation is constructed for pure SU(N) gauge theory in the large N limit. In this way we make precise and concrete the notion of a non-perturbative gauge invariant…
Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…
We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extending previous results known for Gaussian measures. Actually, our result apply beyond the case…
Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that…
This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…
We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that…
We continue development of the theory of contractive Markov systems initiated in \cite{Wer1}. In this paper, we construct the coding map for Feller contractive Markov systems. This allows us to prove a generalization of Ledrappier's Theorem…
We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…
Initially motivated by Hrushovski's paper on definability patterns, we obtain homeomorphisms between Ellis semigroups related to natural actions of the automorphism groups of first order structures and certain collections of types and…
We provide a framework to derive a variational formulation for $-\log\mathbb{E}_\nu\left[e^{-f}\right]$ for a large class of measures $\nu$. We use a family of perturbations of the identity $(W^u)$ whose invertibility we characterize thanks…