2 Algorithm for Fp, p > 2 2 2.1 Alternate formulation of Chernoff bound . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Returning to proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Digression on Perfect Hashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Finishing proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . ...

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subse...

Stancu type operators play a crucial role in convergence estimates. The present article concerns the estimates for certain Kantorovich operators. We first establish some direct formulas giving local approximation theorem, Voronovskaja asymptotic formula, bound second central moment with curtailment, and global theorem by means of modulus continuity Ditzian-Totik Modulus smoothness. also study d...

In this paper we establish an L∞-bound for the Neumann problem of the Poisson equations. We first develop some estimates for the bounds of solutions in several spaces using Poincarés inequality, Trace theorem and Sobolev’s embedding theorem, and then prove our main theorem utilizing the De Giorgi-Nash estimates.

In this paper, we study the two weight commutators theorem of Riesz potential on an arbitrary homogeneous group H dimension N. Moreover, in accordance with results Euclidean space, acquire quantitative weighted bound group.

We prove the local minimality of halfspaces in Carnot groups for a class nonlocal functionals usually addressed as perimeters. Moreover, which De Giorgi’s rectifiability theorem holds, we provide lower bound ?-liminf rescaled energy terms horizontal perimeter.

We consider recurrent diffusive random walks on a strip. present constructive conditions Green functions of finite sub-domains which imply Central Limit Theorem with polynomial error bound, Local Theorem, and mixing environment viewed by the particle process. Our can be verified for wide class environments including independent environments, quasiperiodic are asymptotically constant at infinity...

We correct a bound in the definition of approximate truthfulness used body paper Jackson and Sonnenschein (2007). The proof their main theorem uses different permutation-based definition, implicitly claiming that permutation-version implies bound-based version. show this claim holds only if is loosened. new still strong enough to guarantee fraction lies vanishes as number problems grows, so sta...

We present a short and elementary proof of the Ajtai–Komlós–Tusnády (AKT) optimal matching theorem in dimension 2 via Fourier analysis smoothing argument. The upper bound applies to more general families samples, including dependent variables, interest study rates convergence for empirical measures. Following recent pde approach by L. Ambrosio, F. Stra D. Trevisan, we also adapt simple lower bo...