Related papers: Iterated multiplication in $VTC^0$
The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.
The Temperley-Lieb (TL) family of algebras is well known for its role in building integrable lattice models. Even though a proof is still missing, it is agreed that these models should go to conformal field theories in the thermodynamic…
We give a method of solution to the problem of iterating holomorphic functions to fractional or complex heights. We construct an auxiliary function from natural iterates of a holomorphic function; the auxiliary function will be…
Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…
Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…
We study complexified elliptic Calogero-Moser integrable systems. We determine the value of the potential at isolated extrema, as a function of the modular parameter of the torus on which the integrable system lives. We calculate the…
Generalizing the notion of a multiplicative unitary (in the sense of Baaj-Skandalis), which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a multiplicative partial isometry.…
We prove a structure theorem for multiplicative functions which states that an arbitrary bounded multiplicative function can be decomposed into two terms, one that is approximately periodic and another that has small Gowers uniformity norm…
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the…
We generalize the Umbral Calculus of G-C. Rota by studying not only sequences of polynomials and inverse power series, or even the logarithms studied in, but instead we study sequences of formal expressions involving the iterated logarithms…
Consider multiple sums $S_n$ on the $d$-dimensional integer grid,which are generated by i.i.d.\ random variables with a positive expectation. We prove the strong law of large numbers, the law of the iterated logarithm and the distributional…
The provability logic of a theory $T$ captures the structural behavior of formalized provability in $T$ as provable in $T$ itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…
An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…
The boxdot conjecture asserts that every normal modal logic that faithfully interprets T by the well-known boxdot translation is in fact included in T. We confirm that the conjecture is true. More generally, we present a simple semantic…
By a new method derived from Nicola--Primo--Tabacco[24], we study the boundedness on $\alpha$-modulation spaces of unimodular multipliers with symbol $e^{i\mu(\xi)}$. Comparing with the previous results, the boundedness result is…
Every cluster-tilted algebra $B$ is the relation extension $C\ltimes \text{Ext}^2_C(DC,C)$ of a tilted algebra $C$. A $B$-module is called induced if it is of the form $M\otimes_C B$ for some $C$-module $M$. We study the relation between…
We show how multiplier ideals can be used to obtain uniform multiplicative bounds for certain families of ideals on a smooth complex algebraic variety. In particular we prove a quick but rather surprising result about symbolic powers of…
Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined.