Related papers: Freezing Limits for Beta-Cauchy Ensembles

We study the weak limits of solutions to SDEs \[dX_n(t)=a_n\bigl(X_n(t)\bigr)\,dt+dW(t),\] where the sequence $\{a_n\}$ converges in some sense to $(c_- 1\mkern-4.5mu\mathrm{l}_{x<0}+c_+ 1\mkern-4.5mu\mathrm{l}_{x>0})/x+\gamma\delta_0$.…

This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and P\"otscher (2007). More specifically, their…

We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving…

We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…

The normalization of Bethe eigenstates for the totally asymmetric simple exclusion process on a ring of $L$ sites is studied, in the large $L$ limit with finite density of particles, for all the eigenstates responsible for the relaxation to…

We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…

Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly…

We call "Dyson process" any process on ensembles of matrices in which the entries undergo diffusion. We are interested in the distribution of the eigenvalues (or singular values) of such matrices. In the original Dyson process it was the…

The main goal of the paper is to prove central limit theorems for the magnetization rescaled by $\sqrt{N}$ for the Ising model on random graphs with $N$ vertices. Both random quenched and averaged quenched measures are considered. We work…

In the classical $\beta$-ensembles of random matrix theory, setting $\beta = 2 \alpha/N$ and taking the $N \to \infty$ limit gives a statistical state depending on $\alpha$. Using the loop equations for the classical $\beta$-ensembles, we…

We provide a continuous time limit analysis for the class of Ensemble Square Root Filter algorithms with deterministic model perturbations. In the particular linear case, we specify general conditions on the model perturbations implying…

A Bessel field $\mathcal{B}=\{\mathcal{B}(\alpha,t), \alpha\in\mathbb{N}_0, t\in\mathbb{R}\}$ is a two-variable random field such that for every $(\alpha,t)$, $\mathcal{B}(\alpha,t)$ has the law of a Bessel point process with index…

For a beta-Jacobi ensemble determined by parameters a_1, a_2 and n, under the restriction that the three parameters go to infinity with n and a_1 being of small orders of a_2, we obtain both the bulk and the edge scaling limits. In…

We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…

We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied…

Highly stable laser sources based on narrow atomic transitions provide a promising platform for direct generation of stable and accurate optical frequencies. Here we investigate a simple system operating in the high-temperature regime of…

We address the question of a Berry Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial…

We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…

We carry out the asymptotic analysis of repulsive ensembles of N particles which are discrete analogues of continuous 1d log-gases or beta-ensembles of random matrix theory. The ensembles that we study have several groups of particles which…

The purpose of this paper is to introduce the construction of a stochastic process called "$\delta$-dimensional Bessel house-moving" and its properties. We study the weak convergence of $\delta$-dimensional Bessel bridges conditioned from…