相关论文: Block regularisation of the logarithm central prob…
This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure It\^o and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
Classical approach to regularization is to design norms enhancing smoothness or sparsity and then to use this norm or some power of this norm as a regularization function. The choice of the regularization function (for instance a power…
Within the context of the functional renormalization group flow of gravity, we suggest that a generic f(R) ansatz (i.e. not truncated to any specific form, polynomial or not) for the effective action plays a role analogous to the local…
We consider the Cahn-Hilliard equation with constant mobility and logarithmic potential on a two-dimensional evolving closed surface embedded in $\mathbb R^3$, as well as a related weighted model. The well-posedness of weak solutions for…
We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…
In this paper, we consider the existence and multiplicity of solutions for the logarithmic Schr\"{o}dinger equation on lattice graphs $\mathbb{Z}^N$ $$ -\Delta u+V(x) u=u \log u^2, \quad x \in \mathbb{Z}^N, $$ When the potential $V$ is…
We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows to describe the effective potential as a function of both scalar field…
The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than…
A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
We consider a simplified Boltzmann equation: spatially homogeneous, two-dimensional, radially symmetric, with Grad's angular cutoff, and linearized around its initial condition. We prove that for a sufficiently singular velocity cross…
To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…
In this note we study the error term R_{n,L}(x) in the generalized circle problem for a ball of volume x and a random lattice L of large dimension n. Our main result is the following functional central limit theorem: Fix an arbitrary…
We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity may not.
In this paper, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whose derivative is analytic and a finite sum of terms involving…
Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…
In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…