Related papers: Baxter permuton and Liouville quantum gravity
Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has its roots in string theory and conformal field theory from the 1980s and 1990s. The…
Kenyon, Miller, Sheffield, and Wilson (2015) showed how to encode a random bipolar-oriented planar map by means of a random walk with a certain step size distribution. Using this encoding together with the mating-of-trees construction of…
We introduce a one-parameter family of random infinite quadrangulations of the half-plane, which we call the uniform infinite half-planar quadrangulations with skewness (UIHPQ$_p$ for short, with $p\in[0,1/2]$ measuring the skewness). They…
We conformally weld (via "quantum zipping") two boundary arcs of a Liouville quantum gravity random surface to generate a random curve called the Schramm-Loewner evolution (SLE). We develop a theory of quantum fractal measures (consistent…
We study Liouville quantum gravity (LQG) surfaces whose law has been reweighted according to nesting statistics for a conformal loop ensemble (CLE) relative to $n\in \mathbb{N}_0$ marked points $z_1,\dots,z_n$. The idea is to consider a…
We study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in…
Guibert and Linusson introduced the family of doubly alternating Baxter permutations, i.e. Baxter permutations $\sigma \in S_n$, such that $\sigma$ and $\sigma^{-1}$ are alternating. They proved that the number of such permutations in…
Recent works have shown that random triangulations decorated by critical ($p=1/2$) Bernoulli site percolation converge in the scaling limit to a $\sqrt{8/3}$-Liouville quantum gravity (LQG) surface (equivalently, a Brownian surface)…
We construct a Lebesgue measure preserving natural extension of the random beta-transformation. This allows us to give a formula for the density of the absolutely continuous invariant probability measure, answering a question of Dajani and…
We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $\theta \in \mathbb{R}^d$, and which include multivariate skew normal…
We introduce and study a new random permutation model that generalizes the $k$-card minimum model defined by Travers and the Mallows model. We calculate the permuton limit of such a sequence of random permutations. As a corollary, we deduce…
We study Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which has background charge $Q \in (0,2)$ and central charge $\mathbf{c}_{\mathrm{L}} = 1+6Q^2 \in (1,25)$. Recent works have shown how to define…
We give a thorough description of the asymptotic property of the maximum likelihood estimator (MLE) of the skewness parameter of a Skew Brownian Motion (SBM). Thanks to recent results on the Central Limit Theorem of the rate of convergence…
We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by…
Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton…
We introduce the notion of Bartlett spectral measure for isometrically invariant random measures on proper metric commutative spaces. When the underlying Gelfand pair corresponds to a higher-rank, connected, simple matrix Lie group with…
The ``Brownian bees'' model describes an ensemble of $N=$~const independent branching Brownian particles. The conservation of $N$ is provided by a modified branching process. When a particle branches into two particles, the particle which…
The search for scale-invariant random geometries is central to the Asymptotic Safety hypothesis for the Euclidean path integral in quantum gravity. In an attempt to uncover new universality classes of scale-invariant random geometries that…
Suppose we choose a permutation $\pi$ uniformly at random from $S_n$. Let $\mathsf{runsort}(\pi)$ be the permutation obtained by sorting the ascending runs of $\pi$ into lexicographic order. Alexandersson and Nabawanda recently asked if the…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…