相关论文: An elementary approach to quantum length of SLE
The symmetric binary perceptron ($\mathrm{SBP}_{\kappa}$) problem with parameter $\kappa : \mathbb{R}_{\geq1} \to [0,1]$ is an average-case search problem defined as follows: given a random Gaussian matrix $\mathbf{A} \sim…
We derive local estimates of positive solutions to the conformal $Q$-curvature equation $$ (-\Delta)^m u = K(x) u^{\frac{n+2m}{n-2m}} ~~~~~~ in ~ \Omega \backslash \Lambda $$ near their singular set $\Lambda$, where $\Omega \subset…
We describe the deformed covariant phase space corresponding to the so-called kappa-deformation of D=4 relativistic symmetries, with quantum ``time'' coordinate and Heisenberg algebra obtained according to the Heisenberg double…
Developing the theory of two-sided radial and chordal $\mathit{SLE}$, we prove that the natural parametrization on $\mathit{SLE}_{\kappa}$ curves is well defined for all $\kappa<8$. Our proof uses a two-interior-point local martingale.
A quantum deformation of the conformal algebra of the Minkowskian spacetime in $(3+1)$ dimensions is identified with a deformation of the $(4+1)$-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are…
We study the topology of $SLE$ curves for $\kappa > 4$. More precisely, we show that, a.s., there is no homeomorphism $\Phi: \overline{\mathbb{H}} \rightarrow \overline{\mathbb{H}}$, taking the range of one independent $SLE$ curve to…
In this paper we have studied the nature of kinematical and dynamical laws in $\kappa $-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of $\kappa$-Minkowski phase space algebra…
Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's…
In this short note, based on the talk given at the 3rd Conference of the Polish Society on Relativity, I present the basic points of our recent paper "Symmetries of quantum spacetime in three dimensions", stressing their physical meaning,…
We present an analytic result for the 1-loop quantum mass correction in semiclassical quantization for the twisted \phi^4 kink on S^1 without explicit knowledge of the fluctuation spectrum. For this purpose we use the contour integral…
A useful concept in the development of physical models on the $\kappa$-Minkowski noncommutative spacetime is that of a curved momentum space. This structure is not unique: several inequivalent momentum space geometries have been identified.…
In this paper, we consider the CPE conjecture in the frame-work of $K$-contact and $(\kappa, \mu)$-contact manifolds. First, we prove that if a complete $K$-contact metric satisfies the CPE is Einstein and is isometric to a unit sphere…
We propose new noncommutative models of quantum phase spaces, containing a pair of $\kappa$-deformed Poincar\'e algebras, with two independent double ($\kappa,\tilde{\kappa}$)-deformations in space-time and four-momenta sectors. The first…
In this paper we suggest that the Planck length $l_{pl}$ and the Cosmological Constant scale $r_\Lambda=\frac{1}{\sqrt{\Lambda}}$ could in principle be dual each other if we take seriously the so-called q-Bargmann Fock space representation…
The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…
We have performed a new exact evaluation of the fluctuation determinant $\kappa$ of the electroweak sphaleron with $\Theta _W =0$. The results differ significantly from a previous calculation of this quantity by Carson et. al. . We find…
A new unitarization approach is discussed and applied to study the elastic $\pi K$ scattering process. The existence of the light $\kappa$ resonance is firmly established if the scattering length in the I=1/2 channel does not deviate too…
We compare two versions of deformed dispersion relations (energy vs momenta and momenta vs energy) and the corresponding time delay up to the second order accuracy in the quantum gravity scale (deformation parameter). A general framework…
In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in…
We obtain the $\kappa$-deformed versions of the retarded and advanced Green functions and show that their causality properties are blurred in a time interval of the order of a length parameter $q=1/(2\kappa)$. The functions also indicate a…