Related papers: Well-posedness of the Iterative Boltzmann Inversio…
We study the Busemann process and competition interfaces of the planar directed polymer model with i.i.d.\ weights on the vertices of the planar square lattice, in both the general case and the solvable inverse-gamma case. We prove new…
[abridged] Inversion techniques are the most powerful methods to obtain information about the thermodynamical and magnetic properties of solar and stellar atmospheres. In the last years, we have witnessed the development of highly…
It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space…
We describe a family of iterative algorithms that involve the repeated execution of discrete and inverse discrete Fourier transforms. One interesting member of this family is motivated by the discrete Fourier transform uncertainty principle…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the…
Given a Taylor series with a finite radius of convergence, its Borel transform defines an entire function. A theorem of P\'olya relates the large d istance behavior of the Borel transform in different directions to singularities of the…
In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…
Below the normalized weighted reciprocal of the Christoffel function with respect to exceptional Jacobi polynomials is investigated. It is proved that it tends to the equilibrium measure of the interval of orthogonality in weak-star sense.…
The Boltzmann machine is one of the various applications using quantum annealer. We propose an application of the Boltzmann machine to the kernel matrix used in various machine-learning techniques. We focus on the fact that shift-invariant…
Electrostatic correlations and fluctuations in ionic systems can be described within an extended Poisson-Boltzmann theory using a Gaussian variational form. The resulting equations are challenging to solve because they require the solution…
Within path sampling framework, we show that probability distribution divergences, such as the Chernoff information, can be estimated via thermodynamic integration. The Boltzmann-Gibbs distribution pertaining to different Hamiltonians is…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
A recent solution of the inelastic Boltzmann equation that applies for strong dissipation and takes into account non-equipartition of energy is used to derive an explicit expression for the thermal diffusion factor. This parameter provides…
We make precise sense of the idea of "molecular chaos" through algorithmic randomness of microscopic trajectories, and ground macroscopic irreversibility in the lack of symmetry under time reversal of this property. This concept of…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…
This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…