Related papers: A smooth transition from Wishart to GOE
The full parameter space of the transition from Townsend to glow discharge is investigated numerically in one space dimension in the classical model: with electrons and positive ions drifting in the local electric field, impact ionization…
We study the problem of computing the Fr\'echet distance between two polygonal curves under transformations. First, we consider translations in the Euclidean plane. Given two curves $\pi$ and $\sigma$ of total complexity $n$ and a threshold…
The transition from n = 0 to n = 2 is revealed where n is the number of components of ordering field. The critical exponents are estimated. In frameworks of scaling theory of phase transitions and critical phenomena the results obtained are…
By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an…
Nature of the phase transition of regularly frustrated vector spin systems in three dimensions is investigated based on a Ginzburg-Landau-type effective Hamiltonian. On the basis of the variational analysis of this model, Onoda et al…
We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the…
Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention…
In various approaches to quantum gravity continuum spacetime is expected to emerge from discrete geometries through a phase transition. In group field theory, various indications for such a transition have recently been found but a complete…
The phase transition temperature for the Bose-Einstein condensation (BEC) of weakly-interacting Bose gases in three dimensions is known to be related to certain non-universal properties of the phase transition of three-dimensional O(2)…
We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In…
Orbital degrees of freedom shape many of the properties of a wide class of Mott insulating, transition metal oxides with partially filled 3d-shells. Here we study orbital ordering transitions in systems where a single electron occupies the…
Products of $M$ i.i.d. random matrices of size $N \times N$ are related to classical limit theorems in probability theory ($N=1$ and large $M$), to Lyapunov exponents in dynamical systems (finite $N$ and large $M$), and to universality in…
We consider an extension of the Standard Model with a complex singlet scalar, where a global $U(1)$ symmetry is explicitly broken to $\mathbb{Z}_3$ symmetry. We study the two-step electroweak phase transition in the model and find that it…
We construct a four-dimensional supersymmetric QCD in conformal window with a marginally relevant deformation which triggers the spontaneous breaking of (approximate) scale invariance and the subsequent confinement, generating a mass gap,…
For parameters $n,\delta,B,$ and $C$, let $X=(X_{k\ell})$ be the random uniform contingency table whose first $\lfloor n^{\delta} \rfloor $ rows and columns have margin $\lfloor BCn \rfloor$ and the last $n$ rows and columns have margin…
Optimal transport (OT), and in particular the Wasserstein distance, has seen a surge of interest and applications in machine learning. However, empirical approximation under Wasserstein distances suffers from a severe curse of…
Consider the classical Gaussian unitary ensemble of size $N$ and the real Wishart ensemble $W_N(n,I)$. In the limits as $N \to \infty$ and $N/n \to \gamma > 0$, the expected number of eigenvalues that exit the upper bulk edge is less than…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
We show that gaussian quantum fluctuations, even if infinitesimal, are sufficient to destroy the superfluidity of a disordered boson system in 1D and 2D. The critical disorder is thus finite no matter how small the repulsion is between…
A Deformed Gaussian Orthogonal Ensemble (DGOE) which interpolates between the Gaussian Orthogonal Ensemble and a Poissonian Ensemble is constructed. This new ensemble is then applied to the analysis of the chaotic properties of the low…