相关论文: Fluctuations of the number of excursion sets of pl…
When a random field $(X_t, \ t\in {\mathbb R}^2)$ is thresholded on a given level $u$, the excursion set is given by its indicator $~1_{[u, \infty)}(X_t)$. The purpose of this work is to study functionals (as established in stochastic…
The field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…
Random field excursions is an increasingly vital topic within data analysis in medicine, cosmology, materials science, etc. This work is the first detailed study of their Betti numbers in the so-called `sparse' regime. Specifically, we…
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…
We have considered three different "one-body" statistical systems involving Brownian excursions, which possess for fluctuations Kardar-Parisi-Zhang scaling with the critical exponent $\nu=\frac{1}{3}$. In all models imposed external…
We study the limiting fluctuations of the number of sign and level-set clusters of the Gaussian free field on $\mathbb{Z}^d$, $d \ge 3$, that are contained in a large domain. In dimension $d \ge 4$ we prove that the fluctuations are…
We study the transition between Zeeman levels of an arbitrary spin placed into a regular time-dependent field and a random field with the Gaussian distribution. One component of the regular field changes its sign at some moment of time,…
We study the current of particles that move independently in a common static random environment on the one-dimensional integer lattice. A two-level fluctuation picture appears. On the central limit scale the quenched mean of the current…
The correlated motion of electrons in the presence of strong orbital fluctuations and correlations is investigated with respect to magnetic couplings and excitations in an orbitally degenerate ferromagnet. Introduction of the orbital degree…
In melt-blowing very thin liquid fiber jets are spun due to high-velocity air streams. In literature there is a clear, unsolved discrepancy between the measured and computed jet attenuation. In this paper we will verify numerically that the…
We study the decay of connectivity of the subcritical excursion sets of a class of strongly correlated Gaussian fields. Our main result shows that, for smooth isotropic Gaussian fields whose covariance kernel $K(x)$ is regularly varying at…
We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…
We reconsider Ising spins in a Gaussian random field within the replica formalism. The corresponding continuum model involves several coupling constants beyond the single one which was considered in the standard $\phi^4$ theory approach.…
We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an $n \times n$ matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian…
The intermittency of density fluctuations in the solar wind at kinetic scales has been examined using high time resolution Faraday cup measurements from the Spektr-R spacecraft. It was found that the probability density functions (PDFs) of…
It is shown that conductance fluctuations due to phase coherent ballistic transport through a chaotic cavity generically are fractals. The graph of conductance vs. externally changed parameter, e.g. magnetic field, is a fractal with…
Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random…
We describe a formally exact method to calculate the optical conductivity of a one-dimensional system with fluctuating order. For classical phase fluctuations we explicitly determine the optical conductivity by solving two coupled…
We analyze quantum fluctuation effects at the onset of charge or spin density wave order in two-dimensional metals with an incommensurate $2k_F$ wave vector connecting a single pair of hot spots on the Fermi surface. We compute the momentum…
We consider a scalar field governed by an advection-diffusion equation (or a more general evolution equation) with rapidly fluctuating, Gaussian distributed random coefficients. In the white noise limit, we derive the closed evolution…