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We adapt the concept of $\mathcal{K}-$convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions…
We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…
Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…
In a series of recent papers, W. M. Schmidt and L. Summerer developed a new theory by which they recover all major generic inequalities relating exponents of Diophantine approximation to a point in $\mathbb{R}^n$, and find new ones. Given a…
In this paper, we prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in spheres which improves Baker's convergence theorem. In particular, we obtain a new differentiable sphere theorem for submanifolds in…
We propose a new model which describes relativistic hydrodynamics and generalizes the standard Euler system of isentropic perfect fluids. Remarkably, our system admits a convex extension which allows us to transform it to a symmetric…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…
The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and…
We consider a shallow water model in a homogenization framework. For periodic topographies, Craig, Lannes and Sulem have established a consistency result under some non-resonance conditions. In the present contribution, we significantly…
Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We…
We give constructions of some special cases of $[n,k]$ Reed-Solomon codes over finite fields of size at least $n$ and $n+1$ whose generator matrices have constrained support. Furthermore, we consider a generalisation of the GM-MDS…
In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the…
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fej\'er monotonicity condition, in the context of a (local) compactness assumption. Our result is quantitative…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to…
The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex…
In this paper generalization of Jacobi and Gauss-Seidel methods, introduced by Salkuyeh in 2007, is studied. In particular, convergence criteria for these methods are discussed. A generalization of successive overrelaxation~(SOR) method is…
The relativistic method of moments is one of the most successful approaches to extract second order viscous hydrodynamics from a kinetic underlying background. The equations can be systematically improved to higher order, and they have…
For the partial sums formed from a sequence of i.i.d. random variables having a finite absolute p'th moment for some p in (0,2), we extend the recent and striking discovery of Hechner and Heinkel (Journal of Theoretical Probability (2010))…