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We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for…

We present an analysis of the internal velocity structures of the newly identified sub-0.1 pc coherent structures, droplets, in L1688 and B18. By fitting 2D linear velocity fields to the observed maps of velocity centroids, we determine the…

We study theoretically the spatial correlations between the intensities measured at the input and output planes of a disordered scattering medium. We show that at large optical thicknesses, a long-range spatial correlation persists and…

Coherent backscattering (CBS) arises from complex interactions of a coherent beam with randomly positioned particles, which has been typically studied in media with large numbers of scatterers and high opacity. We develop a first-principles…

We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…

Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A…

During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When…

Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a…

The disordering of an initially phase segregated system of finite size, induced by the presence of highly mobile vacancies, is shown to exhibit dynamic scaling in its late stages. A set of characteristic exponents is introduced and computed…

Inspired by recent work on minimizers and gradient flows of constrained interaction energies, we prove that these energies arise as the slow diffusion limit of well-known aggregation-diffusion energies. We show that minimizers of…

We consider a system where dark matter dynamics is enriched by the presence of clustering quintessence in the approximation where the system is effectively reduced to one degree of freedom. We study the corresponding observables up to…

We investigate theoretically the bifurcation scenario for colloidal suspensions subject to a vertical temperature gradient taking into account the effect of sedimentation. In contrast to molecular binary mixtures, here the thermal…

Propagation and tunneling of light through subwavelength photonic barriers, formed by dielectric layers with continuous spatial variations of dielectric susceptibility across the film are considered. Effects of giant heterogeneity-induced…

What distribution of graphical degree sequence is invariant under ``scaling''? Are these graphs always power-law graphs? We show the answer is a surprising ``yes'' for sparse graphs if we ignore isolated vertices, or more generally, the…

The statistical properties of a large number of weakly nonlinear waves can be described in the framework of the Weak Turbulence Theory. The theory is based on the hypothesis of an asymptotically large system. In experiments, the systems…

We demonstrate that structures made of light can be used to coherently control the motion of complex molecules. In particular, we show diffraction of the fullerenes C60 and C70 at a thin grating based on a standing light wave. We prove…

In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest…

Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the…

The impact of gradient noise on training deep models is widely acknowledged but not well understood. In this context, we study the distribution of gradients during training. We introduce a method, Gradient Clustering, to minimize the…

We study fluctuations in a vertically oscillated layer of grains below the critical acceleration for the onset of ordered standing waves. As onset is approached, transient disordered waves with a characteristic length scale emerge and…