相关论文: The arctic circle boundary and the Airy process

Consider $n+m$ nonintersecting Brownian bridges, with $n$ of them leaving from 0 at time $t=-1$ and returning to 0 at time $t=1$, while the $m$ remaining ones (wanderers) go from $m$ points $a_i$ to $m$ points $b_i$. First, we keep $m$…

The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. In this paper, the boundary correspondence and boundary behavior of alpha-harmonic functions are studied,…

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice…

We prove existence of boundary limits of ratios of positive harmonic functions for a wide class of Markov processes with jumps and irregular domains, in the context of general metric measure spaces. As a corollary, we prove uniqueness of…

The Atlantic Meridional Overturning Circulation (AMOC) is often analyzed using low-order box models to understand tipping points. Historically, these studies focus on freshwater flux as the primary bifurcation parameter, treating the…

We show that the second term in the asymptotic expansion as t approaches 0 of the trace of the Dirichlet heat kernel on Lipschitz domains for unimodal L\'evy processes, satisfying some weak scaling conditions, is given by the surface area…

In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…

We study the T-system of type $A_\infty$, also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. Di Francesco and R. Soto-Garrido. Arctic curves of the…

Helfgott and Gessel gave the number of domino tilings of an Aztec Rectangle with defects of size one on the boundary of one side. In this paper we extend this to the case of domino tilings of an Aztec Rectangle with defects on all boundary…

The fluctuations of lozenge tilings of hexagons with one or several cuts (nonconvexities) along opposite sides are governed by the (discrete-continuous) tacnode kernel ${\mathbb L}^{\mbox{\tiny dTac}}$, upon letting the hexagon become very…

We present a new extended XMM-Newton mosaic of the nearby Coma cluster, which covers the cluster out to the virial radius with nearly complete azimuthal coverage. This large mosaic is combined with the Planck Sunyaev Zel'dovich effect…

A predictive model for the evolution of porous Ge layer upon thermal treatment is reported. We represent an idealized etched dislocation core as an axially symmetric elongated hole and computed its dynamics during annealing. Numerical…

A recent conjecture of Di Francesco states that the number of domino tilings of a certain family of regions on the square lattice is given by a product formula reminiscent of the one giving the number of alternating sign matrices. These…

We consider a generating function of the domino tilings of an Aztec rectangle with several boundary unit squares removed. Our generating function involves two statistics: the rank of the tiling and half number of vertical dominoes as in the…

The horizon structure and thermodynamics of hairy spherically symmetric black holes generated by the gravitational decoupling method are carefully investigated. The temperature and heat capacity of the black hole is determined, as well as…

We use the subgraph replacement method to investigate new properties of the tilings of regions on the square lattice with diagonals drawn in. In particular, we show that the centrally symmetric tilings of a generalization of the Aztec…

In this paper, we prove the boundary partial regularity for a class of coupled Dirac-harmonic maps satisfying a certain energy monotonicity inequality near the boundary.

According to Kumar's recent surprising result (ToCT'20), a small border Waring rank implies that the polynomial can be approximated as a sum of a constant and a small product of linear polynomials. We prove the converse of Kumar's result…

We prove that the boundary of an orbit space or more generally a leaf space of a singular Riemannian foliation is an Alexandrov space in its intrinsic metric, and that its lower curvature bound is that of the leaf space. A rigidity theorem…

We study a parabolic Ventsell problem for a second order differential operator in divergence form and with interior and boundary drift terms on the snowflake domain. We prove that under standard conditions a related Cauchy problem possesses…