Related papers: Characteristic Polynomials of Random Matrices and …

Fractional Brownian motion (fBm) is an important scale-invariant Gaussian non-Markovian process with stationary increments, which serves as a prototypical example of a system with long-range temporal correlations and anomalous diffusion.…

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…

Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center…

We introduce a class of Markov coalescent processes on the continuous $d$-dimensional torus, in the most general setting of simultaneous multiple mergers, called the Brownian spatial coalescent. It is axiomatically defined through a…

The process $(G_t)_{t\in[0,T]}$ is referred to as a fractional Gaussian process if the first-order partial derivative of the difference between its covariance function and that of the fractional Brownian motion $(B^H_t)_{t\in[0,T ]}$ is a…

As a special example of piecewise deterministic Markov process, bouncy particle sampler is a rejection-free, irreversible Markov chain Monte Carlo algorithm and can draw samples from target distribution efficiently. We generalize bouncy…

A random matrix ensemble incorporating both GUE and Poisson level statistics while respecting $U(N)$ invariance is proposed and shown to be equivalent to a system of noninteracting, confined, one dimensional fermions at finite temperature.

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC)…

Consider Dyson's Hermitian Brownian motion model after a finite time S, where the process is started at N equidistant points on the real line. These N points after time S form a determinantal process and has a limit as N tends to infinity.…

Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst…

We study $n$ non-intersecting Brownian motions, corresponding to the eigenvalues of an $n\times n$ Hermitian Brownian motion. At the boundary of their limit shape we find that only three universal processes can arise: the Pearcey process…

There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…

Let $T_{c,\beta}$ denote the smallest $t\ge1$ that a continuous, self-similar Gaussian process with self-similarity index $\alpha>0$ moves at least $\pm c t^\beta$ units. We prove that: (i) If $\beta>\alpha$, then $T_{c,\beta}=\infty$ with…

The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for…

We consider the $1$-dimensional reflected Brownian motion and $3$-dimensional Bessel process and the general models. By decomposing the hitting times of consecutive sites into loops, we obtain identities, called loop identities, for the…

We study expectations of powers and correlation functions for characteristic polynomials of $N \times N$ non-Hermitian random matrices. For the $1$-point and $2$-point correlation function, we obtain several characterizations in terms of…

Inspired by the theory of quantum information, I use two non-Hermitian random matrix models - a weighted sum of circular unitary ensembles and a product of rectangular Ginibre unitary ensembles - as building blocks of three new products of…

We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{\alpha-1}$, $\alpha>0$ (scaled Brownian motion), is stochastically reset to its initial position and…

We study the characteristic polynomial of random permutation matrices following some measures which are invariant by conjugation, including Ewens' measures which are one-parameter deformations of the uniform distribution on the permutation…