相关论文: On the finite pair correlation function of van der…
We show that the de Bruijn-Erd\H{o}s condition for the error term in their improvement of Fekete's Lemma is not only sufficient but also necessary in the following strong sense. Suppose that given a sequence $0\leq f(1)\leq f(2)\leq…
For $0<\theta<1$, we show that for almost all $\alpha$, the pair correlation function of the sequence of fractional parts of $\{\alpha n^\theta:n\geq 1 \}$ is Poissonian.
Given a function f with an absolutely convergent Fourier series, we define the norm of f as ||f||_A = the sum of absolute values of the Fourier coefficients of f. We study the behavior of ||f^n||_A as n goes to infinity, for f of the form…
We consider relations with no order on their attributes as in Database Theory. An independent partition of the set of attributes S of a finite relation R is any partition X of S such that the join of the projections of R over the elements…
A necessary and sufficient condition on the precompactness of extremal sequences for one dimensional $\alpha$-Strichartz inequalities, equivalently $\alpha$-Fourier extension estimates, is established based on the profile decomposition…
Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is…
In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…
Exact relations are derived for the Fermi Hubbard spectral weight function for infinite U at zero temperature in the thermodynamic limit for any dimension,any lattice structure and general hopping matrix. These relations involve moments of…
A sequence $(x_n)_{n=1}^{\infty}$ on the torus $\mathbb{T}$ exhibits Poissonian pair correlation if for all $s\geq0$, \begin{equation*} \lim_{N\to\infty} \frac{1}{N}\#\left\{1\leq m\neq n \leq N : |x_m-x_n| \leq \frac{s}{N}\right\} = 2s.…
In this paper, we derive some new combinatorial inequalities by applying well known real analytic results like H\"{o}lder's inequality, Young's inequality, and Minkowiski's inequality to the recursively defined sequence $f_n$ of functions…
In this note we study the $\sigma$-pair correlation density \begin{equation*}R_2^\sigma([a,b], \{ \theta_n \}_n, N)= \frac{1}{N^{2-\sigma}} \# \big \{ 1 \leq j \neq k \leq N \, \big| \, \theta_{j} - \theta_{k} \in \big […
Finite temperature correlation functions in integrable quantum field theories are formulated only in terms of the usual, temperature-independent form factors, and certain thermodynamic filling fractions which are determined from the…
We investigate expansions for connectedness functions in the random connection model of continuum percolation in powers of the intensity. Precisely, we study the pair-connectedness and the direct-connectedness functions, related to each…
Given a system of functions $\textup{\textbf{F}}=(F_1,\ldots,F_d),$ analytic on a neighborhood of some compact subset $E$ of the complex plane with simply connected complement, we define a sequence of vector rational functions with common…
Let $K$ be a compact set with connected complement on the half-plane Re$(s)>0$, and let $f$ be a continuous function on $K$ which is analytic in its interior. We prove that for any parameter $0<\alpha<1, \alpha \neq \frac 1 2$ then $f(s)$…
We consider the so-called simplest correlation function of four infinitely heavy half-BPS operators in planar N=4 SYM in the limit when the operators are light-like separated in a sequential manner. We find a closed-form expression for the…
In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.
We calculate the two-point correlation function <x(t2)x(t1)> for a subdiffusive continuous time random walk in a parabolic potential, generalizing well-known results for the single-time statistics to two times. A closed analytical…
Motivated by recent interests in predictive inference under distribution shift, we study the problem of approximating finite weighted exchangeable sequences by a mixture of finite sequences with independent terms. Various bounds are derived…
We study the correlation functions of a conformally coupled $\phi^4$-interacting theory in AdS$_3$ and its dual CFT$_2$. The one-loop diagram is not expressible in terms of known transcendental functions, but is shown to be expressible as…