相关论文: Symmetries for the gKPZ equation via multi-indices

The analysis of diagonalizable matrices in terms of their so-called isospectral reduction represents a versatile approach to the underlying eigenvalue problem. Starting from a symmetry of the isospectral reduction, we show in the present…

We characterise the chain rule symmetry for the geometric stochastic heat equations in the full subcritical regime for Gaussian and non-Gaussian noises. We show that the renormalised counter-terms that give a solution invariant under…

We generalize the tree doubling and Christofides algorithm, the two most common approximations for TSP, to parameterized approximations for ATSP. The parameters we consider for the respective parameterizations are upper bounded by the…

We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (all scale uniform equivalences). We prove that these equivalences can be…

We derive the renormalised equation for the quasi-generalised KPZ equation with space-time white noise. We complement the program initiated by Gerencs\'er and Hairer for solving quasi-linear equations using regularity structures by an…

We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…

Two new hybrid algorithms are proposed for large-scale linear discrete ill-posed problems in general-form regularization. They are both based on Krylov subspace inner-outer iterative algorithms. At each iteration, they need to solve a…

We observe that Dickey's stabilizing chain can be naturally included into two-dimensional chain of infinitely many copies of equations of KP hierarchy.

We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely discrete equations defined on the square lattice. The first one…

We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the…

We consider three generalizations of the isoperimetric problem to higher codimension and provide results on equilibrium, stability, and minimization.

We introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any…

This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper…

We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. The direct result of this classification is a list of equations containing no…

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures [M. Hairer, A theory of…

This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {\it minimum normalized cuts}/{\it isoperimteric…

In this paper, we introduce a novel integration method of Kardar-Parisi-Zhang (KPZ) equation. It has always been known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical…

We show in this note how the one-dimensional KZP formula obtained by Benjamini and Schramm can be extended to a multidimensional setting.

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing…