Related papers: The normal distribution in some constrained sample…
When extracting cosmological information from power spectrum measurements, we must consider the impact of super-sample density fluctuations whose wavelengths are larger than the survey scale. These modes contribute to the mean density…
We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As an application, we prove that a set of positive measure in…
In the present paper, we study a set that can be treated as a generalised set of subsums for a geometric series. This object was discovered independently in various mathematical aspects. For instance, it is closely related to various…
We explore the phenomenological implications of generalizing measures to a multidimensional multiverse. We consider a simple model in which the vacua are nucleated from a $D$-dimensional parent spacetime through dynamical compactification…
Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…
This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as…
In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on…
We consider the numbers of positive and negative eigenvalues of matrices of squared distances between randomly sampled i.i.d. points in a given metric measure space. These numbers and their limits, as the number of points grows, in fact…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…
As observers of the universe we are physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
We generalize a recent model-independent form factor parameterization derived from rigorous dispersion relations to include constraints from data in the timelike region. These constraints dictate the convergence properties of the…
In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…
Let $\lambda$ be a probability measure on $\mathbb T^{n-1}$ where $n=2$ or 3. Suppose $\lambda$ is invariant, ergodic and has positive entropy with respect to the linear transformation defined by a hyperbolic matrix. We get a measure $\mu $…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
In one dimension, the theory of the $G$-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…