相关论文: Reversibility of Whole-Plane SLE

A complex algebraic surface $S$ is a $\mathbb{Q}$-homology plane if $H_{i}(S,\mathbb{Q})=0$ for $i>0$. The Negativity Conjecture of Palka asserts that $\kappa(K_{X}+\tfrac{1}{2}D)=-\infty$, where $(X,D)$ is a log smooth completion of $S$.…

We introduce and study conjugate reversibility (or $c$-reversibility) in the complex special linear group $\SL(n,\C)$ where an element is conjugate to the inverse of its complex conjugate. We prove that in $\SL(n, \C)$, every $c$-reversible…

We present TRACE, an almost time-reversible hybrid integrator for the planetary N-body problem. Like hybrid symplectic integrators, TRACE can resolve close encounters between particles while retaining many of the accuracy and speed…

The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(kappa;rho) is extended to the setting where the force points can be in the interior of the domain, radial…

We prove that a two-component mirror-symmetric analytic obstacle in the plane is determined by its resonance poles among such obstacles. The proof is essentially the same as in the interior case (part II of the series). A so-called…

We propose a new reverse time migration method for reconstructing extended obstacles in the planar waveguide using acoustic waves at a fixed frequency. We prove the resolution of the reconstruction method in terms of the aperture and the…

We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation…

Given a periodic placement of copies of a tromino (either L or I), we prove co-RE-completeness (and hence undecidability) of deciding whether it can be completed to a plane tiling. By contrast, the problem becomes decidable if the initial…

In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…

Coherent perfect absorption (CPA), also known as time-reversed laser, is a wave phenomenon resulting from the reciprocity of destructive interference of transmitted and reflected waves. In this work we consider quasi one-dimensional lattice…

The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define…

We compute the almost-sure Hausdorff dimension of the double points of chordal SLE_kappa for kappa > 4, confirming a prediction of Duplantier-Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of…

We present an elementary proof establishing the equality of the right and left-sided $\sqrt{\kappa}$-quantum lengths for an SLE$_\kappa$ curve, where $\kappa\in (0,4]$. We achieve this by demonstrating that the$\sqrt{\kappa}$-quantum length…

Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…

We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of…

A stationary subset $S$ of a regular uncountable cardinal $\kappa$ {\it reflects fully} at regular cardinals if for every stationary set $T \subseteq \kappa$ of higher order consisting of regular cardinals there exists an $\alpha \in T$…

We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function. In particular, using an interpretation of this energy as a large deviation rate function for…

Given a separation oracle for a convex set $K \subset \mathbb{R}^n$ that is contained in a box of radius $R$, the goal is to either compute a point in $K$ or prove that $K$ does not contain a ball of radius $\epsilon$. We propose a new…

The study of phase-space constructions based on the properties of the $\kappa$-Poincar\'e Hopf algebra has been a very active area, mostly because of its possible applications in the phenomenology of Planck-scale-induced momentum dependence…

We consider the mirrors model in $d$ dimensions on an infinite slab and with unit density. This is a deterministic dynamics in a random environment. We argue that the crossing probability of the slab goes like $\kappa/(\kappa+N)$ where $N$…