Related papers: A sufficient condition for local limit theorem

We formulate abstract conditions under which a suspension flow satisfies the local central limit theorem. We check the validity of these conditions for several systems including reward renewal processes, Axiom A flows, as well as the…

In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local $\gamma$-, $\epsilon$- and $L$-factors, defined by virtue of the generalized doubling method, over any local field of…

Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…

We establish that for q>=1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of…

Let I_1,...,I_n be independent but not necessarily identically distributed Bernoulli random variables, and let X_n=\sum_{j=1}^nI_j. For \nu in a bounded region, a local central limit theorem expansion of P(X_n=EX_n+\nu) is developed to any…

We prove a local limit theorem the number of $r$-cliques in $G(n,p)$ for $p\in(0,1)$ and $r\ge 3$ fixed constants. Our bounds hold in both the $\ell^\infty$ and $\ell^1$ metric. The main work of the paper is an estimate for the…

We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of…

We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.

Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…

We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear…

We provide several Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior. Our results generalize and improve various known versions of the Ingham-Fatou-Riesz theorem and the Wiener-Ikehara theorem. Using…

Let $\mathcal F=(F, +. \cdot, <, 0, 1, \dots)$ be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several…

The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the $p(x)$-Laplacian posed in $\mathbb{R}^N$. This equation is critical in the sense that the source term has the form…

This paper gives sufficent and necessary conditions on a kind of limit results to hold on the precise convergent rate of an infinite series of probabilities on the Chung type law of the iterated logarithm.

For an optimal control problem, the concept of a strong local infimum is introduce, for which necessary conditions consisting of some family of "maximum principles" are formulated. If a function delivers a strong local minimum in this…

We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…

We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.

In the setting of spaces of homogeneous type, we give a direct proof of the local Tb theorem for singular integral operators. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2,…

In this paper, we establish sufficient conditions for the existence of error bounds at infinity for lower semicontinuous inequality systems. We also show that the existence of an error bound at infinity of constraint systems plays an…

We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…