Related papers: Large deviations of reflected weakly interacting p…
We provide a quantitative asymptotic analysis for the nonlinear Vlasov--Poisson--Fokker--Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often…
The problem of a weak shock, reflected and diffracted by a wedge, is studied for the two-dimensional compressible Euler system. Some recent developments are overviewed and a perspective is presented within the context of a real gas, modeled…
The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. Then for a sequence of these equations, when their coefficients…
The dark-matter candidates of particle physics invariably possess electromagnetic interactions, if only via quantum fluctuations. Taken en masse, dark matter can thus engender an index of refraction which deviates from its vacuum value. Its…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
Weak measurement is a novel technique for parameter estimation with higher precision. In this paper we develop a general theory for the parameter estimation based on weak measurement technique with arbitrary postselection. The previous weak…
In this work, we establish the small-noise asymptotic behaviour (namely, the functional law of large numbers and the large deviation principle) for multi-scale McKean--Vlasov diffusions with super-linear kernels. In this setting, the…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
The essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional…
We introduce a stochastic particle system that corresponds to the Fokker-Planck equation with decay in the many-particles limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an…
Weak measurement is unique in enabling measurements of non-commuting operators as well as otherwise-undetectable peculiar phenomena predicted by the Two-State-Vector-Formalism (TSVF). This article, the first in two parts, explores novel…
We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
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 consider the empirical neighborhood distribution of marked sparse Erd\"os-R\'enyi random graphs, obtained by decorating edges and vertices of a sparse Erd\"os-R\'enyi random graph with i.i.d.\ random elements taking values on Polish…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
Post-selected weak measurement has been widely used in experiments to observe weak effects in various physical systems. However, it is still unclear how large the amplification ability of a weak measurement can be and what determines the…
Reflection statistics have not been well studied for optical random media whose mean refractive indices do not match with the refractive indices of their surrounding media. Here, we theoretically study how this refractive index mismatch…
The Weak Turbulence Theory has been applied to waves in thin elastic plates obeying the F\"oppl-Von K\'arm\'an dynamical equations. Subsequent experiments have shown a strong discrepancy between the theoretical predictions and the…