Related papers: Groups, drift and harmonic measures
We prove that the harmonic measures of certain finite range random walks on Fuchsian Schottky groups, have dimension strictly smaller than the Hausdorff dimension of the corresponding limit set.
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms.…
This exploration of solutions for the orbits of Local Group galaxies under the cosmological initial condition of growing peculiar velocities and fitted to measured distances, redshifts, and proper motions reveals a considerable variety of…
In recent work with Harman, we introduced a new notion of measure for oligomorphic groups, and showed how they can be used to produce interesting tensor categories. Determining the measures for an oligomorphic group is (in our view) an…
Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The…
In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is…
Concept drift -- the change of the distribution over time -- poses significant challenges for learning systems and is of central interest for monitoring. Understanding drift is thus paramount, and drift localization -- determining which…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally H\"older continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…
Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
We study two problems concerning harmonic measure on "champagne subdomains" of the unit disk. These domains are obtained by removing from the unit disk little disks around sequences of points with a uniform distribution with respect to the…
We discuss fluctuations in the measurement process and how these fluctuations are related to the dissipational parameter characterising quantum damping or decoherence. On the example of the measuring current of the variable-barrier or QPC…
In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…
In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.