Related papers: On Tsirelson's theorem about triple points for har…
The Thirring model with random couplings is a translationally invariant generalisation of the SYK model to 1+1 dimensions, which is tractable in the large N limit. We compute its two point function, at large distances, for any strength of…
In bounding the homology of a manifold, Forman's Discrete Morse theory recovers the full precision of classical Morse theory: Given a PL triangulation of a manifold that admits a Morse function with c_i critical points of index i, we show…
Boundary analysis is developed for a rich class of generally infinite weighted graphs with compact metric completions. These graph completions have totally disconnected boundaries. The classical notion of $\epsilon$-components and the…
We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective…
We demonstrate that in a globally deterministic universe, all spatiotemporally symmetric processes must obey counterfactual parameter independence. We show that the Tsirelson bound can be derived from counterfactual parameter independence.…
We study the Hamiltonian for a system of N identical bosons interacting with an impurity, i.e., a different particle, via zero-range forces in dimension three. It is well known that, following the standard approach, one obtains the…
Since the seminal work of Schoen-Uhlenbeck, many authors have studied properties of harmonic maps satisfying Dirichlet boundary conditions. In this article, we instead investigate regularity and symmetry of $\mathbb{S}^2-$valued minimizing…
It is proved that if the points of the three-dimensional Euclidean space are coloured in red and blue, then there exist either two red points unit distance apart, or six collinear blue points with distance one between any two consecutive…
As the main theorem, it is proved that a collection of minimal $PI$-flows with a common phase group and satisfying a certain algebraic condition is multiply disjoint if and only if the collection of the associated maximal equicontinuous…
A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every…
Bell's theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for…
A new class of metric measure spaces is introduced and studied. This class generalises the well-established doubling metric measure spaces as well as the spaces (R^n,mu) with mu(B(x,r))<Cr^d, in which non-doubling harmonic analysis has…
We give a solution of the problem on trigonometric polynomials $f_n$ with the given leading harmonic $y\cos nt$ that deviate the least from zero in measure, more precisely, with respect to the functional $\mu(f_n)=mes\{t\in[0,2\pi]:…
We prove that for any open Riemann surface $M$ and any non constant harmonic function $h:M \to \mathbb{R},$ there exists a complete conformal minimal immersion $X:M \to \mathbb{R}^3$ whose third coordinate function coincides with $h.$ As a…
This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with…
In this work we establish rigorously a measurement uncertainty relation (MUR) for three unbiased qubit observables, which was previously shown to hold true under some presumptions. The triplet MUR states that the uncertainty, which is…
The Three Gap Theorem states that for any $\alpha \in \mathbb{R}$ and $N \in \mathbb{N}$, the fractional parts of $\{ 0\alpha, 1\alpha, \dots, (N - 1)\alpha \}$ partition the unit circle into gaps of at most three distinct lengths. We prove…
We show that a domain in $\mathbb{R}^3$ with the trace of a 3D Brownian motion removed almost surely satisfies the boundary Harnack principle (BHP). Then, we use it to prove that the intersection exponents for 3D Brownian motion are…
In the present paper we prove that for any open connected set $\Omega\subset\mathbb{R}^{n+1}$, $n\geq 1$, and any $E\subset \partial \Omega$ with $\mathcal{H}^n(E)<\infty$, absolute continuity of the harmonic measure $\omega$ with respect…
In this manuscript, we investigate the exponentially harmonic equation on noncompact forward complete Finsler metric measure spaces. We demonstrate that this Finslerian equation represents a critical point of an exponential energy…