Related papers: Infinite measure renewal theorem and related resul…

The possibility of reconciliation between canonical probability distributions obtained from the $q$-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is…

Consider a mixing dynamical systems $([0,1], T, \mu)$, for instance a piecewise expanding interval map with a Gibbs measure $\mu$. Given a non-summable sequence $(m_k)$ of non-negative numbers, one may define $r_k (x)$ such that $\mu (B(x,…

Consider multiple sums $S_n$ on the $d$-dimensional integer grid,which are generated by i.i.d.\ random variables with a positive expectation. We prove the strong law of large numbers, the law of the iterated logarithm and the distributional…

We show that the (Gurevich) topological entropy for the countable Markov shift associated with an infinite transition matrix $A$ coincides with the non-commutative topological entropy for the Exel--Laca algebra associated with $A$, under…

We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by…

We consider a modified Euler equation on $\mathbb R^2$. We prove existence of weak global solutions for bounded (and fast decreasing at infinity) initial conditions and construct Gibbs-type measures on function spaces which are…

Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we derive a key maximal inequality foreshadowed by Robbins,…

In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in ${\mathcal{H}}$ (a real and separable Hilbert space) admits an approximation, in…

We introduce the notions of over- and under-independence for weakly mixing and (free) ergodic measure preserving actions and establish new results which complement and extend the theorems obtained in [BoFW] and [A]. Here is a sample of…

In this paper we study the set of Li-Yorke $d$-tuples and its $d$-dimensional Lebesgue measure for interval maps $T\colon [0,1] \to [0,1]$. If a topologically mixing $T$ preserves an absolutely continuous probability measure 9with respect…

We remark a variant of the existence part of the fundamental theorem of calculus, which, together with the Lebesgue differentiation theorem, constitute a new proof that every Riemann-integrable function on a compact interval having limit…

The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…

Let $\alpha$ be a Steinhaus or a Rademacher random multiplicative function. For a wide class of multiplicative functions $f$ we show that the sum $\sum_{n \le x}\alpha(n) f(n)$, normalised to have mean square $1$, has a non-Gaussian…

We consider continuous maps of the interval which preserve the Lebesgue measure. Except for the identity map or $1 - \id$ all such maps have topological entropy at least $\log2/2$ and generically they have infinite topological entropy. In…

We make the first steps towards an understanding of the ergodic properties of a rational map defined over a complete algebraically closed non-archimedean field. For such a rational map R, we construct a natural invariant probability measure…

Let L be a countable language. We say that a countable infinite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set as M that is invariant under…

We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…

We consider skew extensions of expanding maps by compact Lie groups. For a class of natural invariant measures, we prove an explicit lower bound on the rate of (exponential) mixing involving topological pressure. Proof uses representation…

We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of…

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes, especially stochastic integrals and differential equations. In this paper, general central limit theorems and functional…