Related papers: Bridges and random truncations of random matrices

The $\alpha$-Brownian bridge, or scaled Brownian bridge, is a generalization of the Brownian bridge with a scaling parameter that determines how strong the force that pulls the process back to 0 is. The bias of the maximum likelihood…

We study linear spectral statistics of $N \times N$ Wigner random matrices $\mathcal{H}$ on mesoscopic scales. Under mild assumptions on the matrix entries of $\mathcal{H}$, we prove that after centering and normalizing, the trace of the…

1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates from square shape and becomes more rectangular. 2. If we…

We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which…

We consider two $n\times n$ non-Hermitian random matrices such that the $ij$th entry of one matrix is correlated with the $ij$th entry of the other matrix. However, the entries of any particular matrix are i.i.d. random variables. We study…

We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…

We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…

We consider a Brownian motion with linear drift that splits at fixed time points into a fixed number of branches, which may depend on the branching point. For this process, which we shall refer to as the Brownian decision tree, we…

The classical random graph model $G(n,\lambda/n)$ satisfies a `duality principle', in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved…

For every integer $n\geq 1$, we consider a random planar map $\mathcal{M}_n$ which is uniformly distributed over the class of all rooted bipartite planar maps with $n$ edges. We prove that the vertex set of $\mathcal{M}_n$ equipped with the…

We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…

We present a simple solution to a question posed by Candes, Romberg and Tao on the uniform uncertainty principle for Bernoulli random matrices. More precisely, we show that a rectangular k*n random subgaussian matrix (with k < n) has the…

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge…

We study mesoscopic linear statistics for a class of determinantal point processes which interpolates between Poisson and Gaussian Unitary Ensemble statistics. These processes are obtained by modifying the spectrum of the correlation kernel…

We investigate how the choice of spatial point process for generating random sampling patterns affects the numerical stability of non-uniform generalized sampling between Fourier bases and Daubechies scaling functions. Specifically, we…

This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

In this paper we investigate the behavior of the bridges of a Markov counting process in several directions. We first characterize convexity(concavity) in time of the mean value in terms of lower (upper) bounds on the so called…

In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…

We consider the equilibrium surface of the Random Average Process started from an inclined plane, as seen from the height of the origin, obtained in [Ferrari & Fontes, 1998], where its fluctuations were shown to be of order of the square…