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Related papers: The arctic circle boundary and the Airy process

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The parabolic Airy process is the Airy$_2$ process minus a parabola, initially defined by its finite-dimensional distributions, which are given by a Fredholm determinant formula with the extended Airy kernel. This process is also the…

Probability · Mathematics 2025-07-29 Zhipeng Liu , Aaron Ortiz

The "edge" of the Antarctic polar vortex is known to behave as a barrier to the meridional (poleward) transport of ozone during the austral winter. This chemical isolation of the polar vortex from the middle and low latitudes produces an…

Geophysics · Physics 2015-05-18 Naratip Santitissadeekorn , Gary Froyland , Adam Monahan

Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo -- a key parameter in climate…

Pattern Formation and Solitons · Physics 2017-11-28 Ivan Sudakov , Sergey A. Vakulenko , Kenneth M. Golden

We report new observations of multiple transitions of the CS molecular lines in the SgrA region of the Galactic center, at an angular resolution of 40" (=1.5 pc). The objective of this paper is to study the polar arc, which is a molecular…

Astrophysics of Galaxies · Physics 2015-10-13 Pei-Ying Hsieh , Paul T. P. Ho , Chorng-Yuan Hwang

We revisit the problem of determining the Arctic curve in the six-vertex model with domain wall boundary conditions. We describe an alternative method, by which we recover the previously conjectured analytic expression in the square domain.…

Mathematical Physics · Physics 2016-11-07 Filippo Colomo , Andrea Sportiello

We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point on the arctic boundary, that is not a cusp or tangency…

Probability · Mathematics 2025-02-19 Amol Aggarwal , Jiaoyang Huang

In this paper we consider the six-vertex model at ice point on an arbitrary three-bundle domain, which is a generalization of the domain-wall ice model on the square (or, equivalently, of a uniformly random alternating sign matrix). We show…

Probability · Mathematics 2022-02-17 Amol Aggarwal

A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches…

Probability · Mathematics 2019-05-20 Steven Delvaux , Bálint Vető

This paper presents a detailed analysis of the heat kernel on an $(\mathbb{N}\times\mathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, uniform bounds of the heat…

Probability · Mathematics 2020-03-06 Patricia Alonso Ruiz

We consider a discrete polynuclear growth (PNG) process and prove a functioal limit theorem for its convergrence to the Airy process. This generalizes previous results by Pr"ahofer and Spohn. The result enables us to express the GOE largest…

Probability · Mathematics 2009-11-07 Kurt Johansson

On a finite weighted graph, the dimer model is a probability measure on its dimer covers, that assigns to any cover a probability proportional to the product of the weights of its edges. For planar bipartite graphs, dimer correlations are…

Probability · Mathematics 2026-05-06 Tomas Berggren , Alexei Borodin , Terrence George

A better understanding of the ice-ocean couplings is required to better characterise the hydrosphere of the icy moons. Using global numerical simulations in spherical geometry, we have investigated here the interplay between rotating…

Earth and Planetary Astrophysics · Physics 2024-12-16 T. Gastine , B. Favier

Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…

Statistical Mechanics · Physics 2021-03-17 Jean-Marie Stéphan

In the paper arXiv:1803.11463, the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for…

Mathematical Physics · Physics 2020-01-30 Bryan Debin , Philippe Ruelle

We study the asymptotic behavior of random dimer coverings of the one-periodic Aztec diamond in random environment. We investigate quenched limit theorems for the height function and we extend annealed limit theorems that were recently…

Probability · Mathematics 2025-10-15 Panagiotis Zografos

We study higher limits over the centric orbit category of a fusion system realized by an amalgamated product. In so doing we provide a novel technique for studying the Diaz-Park sharpness conjecture and prove it (in the case of the…

Algebraic Topology · Mathematics 2026-01-22 Marco Praderio Bova

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a…

Probability · Mathematics 2007-05-23 Craig A. Tracy , Harold Widom

The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions…

Mathematical Physics · Physics 2011-06-27 F. Colomo , A. G. Pronko

Using the polar decomposition of a bounded linear operator $A$ defined on a complex Hilbert space, we obtain several numerical radius inequalities of the operator $A$, which generalize and improve the earlier related ones. Among other…

Functional Analysis · Mathematics 2023-03-07 Pintu Bhunia

We investigate the connection between lozenge tilings and domino tilings by introducing a new family of regions obtained by attaching two different Aztec rectangles. We prove a simple product formula for the generating functions of the…

Combinatorics · Mathematics 2015-09-30 Tri Lai