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We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution…
We establish laws of the iterated logarithm for intrinsic volumes of the convex hull of many-step, multidimensional random walks whose increments have two moments and a non-zero drift. Analogous results in the case of zero drift, where the…
The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these…
We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and…
We evaluate the influence functional for two dimensional models of dilaton gravity. This functional is exactly computed when the conformal invariance is preserved, and it can be written as the difference between the Liouville actions on…
In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
We show that convexity of the effective action follows from its functional flow equation. Our analysis is based on a new, spectral representation. The results are relevant for the study of physical instabilities. We also derive constraints…
A complete classification of all zonal, continuous, and translation invariant valuations on convex bodies is established. The valuations obtained are expressed as principal value integrals with respect to the area measures. The convergence…
This paper explores the interactions of absolute continuity of the (quasi)norm with the concepts that are fundamental in the theory of rearrangement-invariant (quasi-)Banach function spaces, such as the Luxemburg representation or the…
We study concave trace functions of several operator variables and formulate and prove multivariate generalisations of the Golden-Thompson inequality. The obtained results imply that certain functionals in quantum statistical mechanics have…
Hajek's stochastic comparison result is generalised to multivariate stochastic sum processes with univariate convex data functions and for univariate monoton nondecreasing convex data functions for processes with and without drift…
A fundamental open question asking whether all real-valued strongly quasiconvex functions defined on $\mathbb R^n$ are necessarily continuous, akin to their convex counterparts, is answered in detail in this paper. Among other things, we…
This paper introduces the proper notion of variational quasiconvexity associated to a group of diffeomorphisms. We prove a lower semicontinuity theorem connected to this notion. In the second part of the paper we apply this result to a…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
We extend to a functional setting the concept of quermassintegrals, well-known within the Minkowski theory of convex bodies. We work in the class of quasi-concave functions defined on the Euclidean space, and with the hierarchy of their…
Under appropriate integrability conditions the risk measure of the sample measures for a law invariant risk measure converge almost surely to the risk measure of the sampled random variable. The results follow from general convergence…
Recent work on recurrence in quantum walks has provided a representation of Schur functions in terms of unitary operators. We propose a generalization of Schur functions by extending this operator representation to arbitrary operators on…