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In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many applications to
We consider the inequality $f geqslant fstar f$ for real integrable functions on $d$ dimensional Euclidean space where $fstar f$ denotes the convolution of $f$ with itself. We show that all such functions $f$ are non-negative, which is not the case f
For hyperbolic flows $varphi_t$ we examine the Gibbs measure of points $w$ for which $$int_0^T G(varphi_t w) dt - a T in (- e^{-epsilon n}, e^{- epsilon n})$$ as $n to infty$ and $T geq n$, provided $epsilon > 0$ is sufficiently small. This is simila
In this note, we study large deviations of the number $mathbf{N}$ of intercalates ($2times2$ combinatorial subsquares which are themselves Latin squares) in a random $ntimes n$ Latin square. In particular, for constant $delta>0$ we prove that $Pr(mat
The paper studies the sampling discretization problem for integral norms on subspaces of $L^p(mu)$. Several close to optimal results are obtained on subspaces for which certain Nikolskii-type inequality is valid. The problem of norms discretization i