اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAsymptotic behavior of Renyi entropy in the central limit theorem
208
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We explore an asymptotic behavior of Renyi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.
قيم البحث
اقرأ أيضاً
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of $n$ independ
ent and identically distributed lattice random variables and an appropriately discretised Gaussian, vanishes as $ntoinfty$.
We prove for the rescaled convolution map $fto fcircledast f$ propagation of polynomial, exponential and gaussian localization. The gaussian localization is then used to prove an optimal bound on the rate of entropy production by this map. As an appl
ication we prove the convergence of the CLT to be at the optimal rate $1/sqrt{n}$ in the entropy (and $L^1$) sense, for distributions with finite 4th moment.
For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become necessary) fo
r the convergence, in transportation, of probability measures when the cost function is continuous, non-decreasing and depends on the distance. As an application, the CLT in the transportation distance is proved for independent and some dependent stationary sequences.
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or time. We fir
st prove that the latter converges, uniformly in compacts in probability, to the solution of an ordinary differential equation, which is explicitly solved. Next, we study the stability properties of its equilibrium points. Moreover, we show that the fluctuations of the proportion of fit individuals, after a proper normalization, satisfy a uniform central limit theorem in $[0,infty)$. As a consequence, we deduce the convergence of the corresponding stationary distributions.
We consider a class of interacting particle systems with values in $[0,8)^{zd}$, of which the binary contact path process is an example. For $d ge 3$ and under a certain square integrability condition on the total number of the particles, we prove a
central limit theorem for the density of the particles, together with upper bounds for the density of the most populated site and the replica overlap.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
