Related papers: A note on Loewner energy, conformal restriction an…

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop…

We revisit the description provided by Ph. Biane of the spectral measure of the free unitary Brownian motion. We actually construct for any $t \in (0,4)$ a Jordan curve $\gamma_t$ around the origin, not intersecting the semi-axis…

In this paper we shall give an analytic proof of the fact that the Liouville energy on a topological two sphere is bounded from below. Our proof does not rely on the uniformization theorem and the Onofri inequality, thus it is essentially…

In this note, we describe our recent results on semiclassical measures for the Schr{\"o}dinger evolution on Zoll manifolds. We focus on the particular case of eigenmodes of the Schr{\"o}dinger operator on the sphere endowed with its…

We study isometric immersions of a Riemannian surface $(\Omega,\frak{g})$, where $\Omega \subset \mathbb{R}^2$, into $\mathbb{R}^3$. We consider their bending energy, i.e., the square of the $L^2$-norm of their second fundamental form,…

The GW approximation for the electronic self-energy is an important tool for the quantitative prediction of excited states in solids, but its mathematical exploration is hampered by the fact that it must, in general, be evaluated…

The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the other analytic in the unbounded complementary component of…

We study the loop $O(n)$ model on the honeycomb lattice. By means of local non-planar deformations of the lattice, we construct a discrete stress-energy tensor. For $n\in [0,2]$, it gives a new observable satisfying a part of Cauchy-Riemann…

We prove that the scaling limit of loop-erased random walk in a simply connected domain $D$ is equal to the radial SLE(2) path in $D$. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the…

We derive recurrence relations for leading logarithmic all-loop quantum corrections in the case of $SO(N)$ symmetric scalar theory with an arbitrary potential in curved spacetime. On this basis, a system of renormalisation group (RG)…

In this paper is considered nonlinear electrodynamics (NE) which does not satisfy the linear superposition principle (LSP). Since the presentation of the special theory of relativity, it has been commonly accepted that a famous formula E =…

We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy…

The generating function method is applied to the trace of the heat kernel and the one-loop effective action derived from the covariant perturbation theory. The basis of curvature invariants of second order for the heat kernel (Green…

We study the problem originally communicated by E. Meckes on the asymptotics for the eigenvalues of the kernel of the unitary eigenvalue process of a random $n \times n$ matrix. The eigenvalues $p_{j}$ of the kernel are, in turn, associated…

We consider a non-linear realization of the electroweak symmetry-breaking pattern $SU(2)_L\times SU(2)_R/SU(2)_{L+R}$ to construct a low-energy effective theory, later extended by the inclusion of heavy new-physics resonances. After…

We consider the effective theory for the low-energy modes of SU(2) gauge theory on the three-sphere. By explicitely integrating out the high-energy modes, the one-loop correction to the hamiltonian for this problem is obtained. We calculate…

A new scheme for the numerical evaluation of the one-loop self-energy correction to all orders in Z \alpha is presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a…

This paper introduces a general construction of self-similar metric spaces as limits of discrete graphs. Our framework produces many classical examples, such as the Sierpi\'nski carpet and the higher dimensional Menger sponges, but also a…

We define the Schramm-Loewner evolution (SLE) in multiply connected domains for kappa \leq 4 using the Brownian loop measure. We show that in the case of the annulus, this is the same measure obtained recently by Dapeng Zhan. We use the…

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in…