Related papers: Correlation Inequality for Formal Series
A generalization of an inequality from IMO is proven.
We show that there exist two proper creature forcings having a simple (Borel) definition, whose product is not proper. We also give a new condition ensuring properness of some forcings with norms.
A new series of correlation inequalities for random field spin systems is proven rigorously. First one corresponds to the well-known Schwartz-Soffer inequality. These are expected to rule out incorrect results calculated in effective…
We obtain some new inequalities of Chebyshev Type.
We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to…
We prove a Korn-type inequality in H(Curl) for tensor fields.
We present a relative form of the Toponogov comparison theorem.
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents of the real numbers corresponding to the differences of…
We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by M. Bertola, B. Dubrovin, D. Yang and by P. Zograf.
This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas
We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
Nonclassical properties of correlations-- like unpredictability, no-cloning and uncertainty-- are known to follow from two assumptions: nonlocality and no-signaling. For two-input-two-output correlations, we derive these properties from a…
We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures.…
Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…
Let G be a finite abelian group of order n. For a complex valued function f on G, let \fht denote the Fourier transform of f. The uncertainty inequality asserts that if f \neq 0 then |supp(f)| |supp(\fht)| \geq n. Answering a question of…
According to Chen and Fu's method, we offer a short proof for Dougall's $_2H_2$-series identity.