Related papers: Erratum: Limit theorems for Betti numbers of rando…

We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.

We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar…

We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is…

We survey recent results on bounds for Betti numbers of modules over polynomial rings, with an emphasis on lower bounds. Along the way, we give a gentle introduction to free resolutions and Betti numbers, and discuss some of the reasons why…

The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (2009) " is flawed. We give here a corrected proof.

Assume the Riemann hypothesis throughout. We obtain some new estimates for the size of the set of large values of the error term in the prime number theorem. Our argument is based on an analysis of the behavior of zeros of the Riemann zeta…

We correct an error in the article "Property (RD) for Hecke pairs".

We correct the proof in the unoriented case of Theorem 1.2 in the paper "Cobordisms of maps with singularities of given class"

Erratum to "From Uncertainty Principles to Wegner Estimates".

We correct a partial mistake for a metric presented in the article "Lattice constellation and codes from quadratic number fields" [IEEE Trans. Inform. Theory, vol. 47, No. 4, May. 2001]. We show that the metric defined in the article is not…

In the erratum we correct a mistake (due to a wrong choice of basic polynomial invariants over Z[1/2]) in the original paper (v1). Using the correct basic polynomial invariants we improve our results and bounds on the annihilator. We also…

Correction to Annals of Probability 28 (2000) 277--302 [doi:10.1214/aop/1019160120].

In this paper, we will give some estimation for the average error of the prime number theorem.

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

This note contains a correction of the proofs of the main results of the paper [A. Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 (2005), 383-432]. The results are correct as originally stated.

We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…

The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…

We correct an error in the second part of Theorem 3 of our original paper (arXiv:1512.07161).

We study the extremal Betti numbers of the class of $t$--spread strongly stable ideals. More precisely, we determine the maximal number of admissible extremal Betti numbers for such ideals, and thereby we generalize the known results for…