Related papers: Multicritical random partitions
We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components.…
The number of sequences of odd length in strict partitions (denoted as $\mathrm{sol}$), which plays a pivotal role in the first paper of this series, is investigated in different contexts, both new and old. Namely, we first note a direct…
The regularity lemma of Szemeredi asserts that one can partition every graph into a bounded number of quasi-random bipartite graphs. In some applications however, one would like to have a strong control on how quasi-random these bipartite…
We construct generalized regular representations of the wreath product of a compact group with the infinite symmetric group. The characters of these representations are determined by probability measures on families of partitions called the…
We consider uniformly random set partitions of size $n$ with exactly $k$ blocks, and uniformly random permutations of size $n$ with exactly $k$ cycles, under the regime where $n-k \sim t\sqrt{n}$, $t>0$. In this regime, there is a simple…
The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on…
In recent studies of many-body localization in nonintegrable quantum systems, the distribution of the ratio of two consecutive energy level spacings, $r_n=(E_{n+1}-E_n)/(E_{n}-E_{n-1})$ or $\tilde{r}_n=\min(r_n,r_n^{-1})$, has been used as…
We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition. We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin…
We explore probabilistic consequences of correspondences between $q$-Whittaker measures and periodic and free boundary Schur measures established by the authors in the recent paper [arXiv:2106.11922]. The result is a comprehensive theory of…
We examine the notion of Haldane's dimension and the corresponding statistics in a probabilistic spirit. Motivated by the example of dimensional-regularization we define the dimension of a space as the trace of a diagonal `unit operator',…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics for the partition functions associated to the Laguerre and Gaussian Unitary Ensembles perturbed with a pole of order $k$ at the origin, in…
A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces are equipped with the Gromov-weak topology and give a new…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist…
We use an injection method to prove a new class of partition inequalities involving certain $q$-products with two to four finitization parameters. Our new theorems are a substantial generalization of work by Andrews and of previous work by…
In the context of generalized measurement theory, the Gleason-Busch theorem assures the unique form of the associated probability function. Recently, in Flatt et al. Phys. Rev. A 96, 062125 (2017), the case of subsequent measurements has…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
This paper deals with the problem of quantifying the approximation a probability measure by means of an empirical (in a wide sense) random probability measure, depending on the first n terms of a sequence of random elements. In Section 2,…
We study the distribution of the largest eigenvalue in the "Pfaffian" classical ensembles of random matrix theory, namely in the Gaussian orthogonal (GOE) and Gaussian symplectic (GSE) ensembles, using semi-classical skew-orthogonal…