Related papers: Non-commutative Laurent phenomenon for two variabl…
We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to…
An alternative proof for existence of ``quantum nonlocality without entanglement'', i.e. existence of variables with product-state eigenstates which cannot be measured locally, is presented. A simple``nonlocal'' variable for the case of…
In this article we prove a Grothendieck trace formula for L-functions of not necessarily commutative adic sheaves.
The non-commutative Central Limit Theorem (CLT) introduced by Speicher in 1992 states that given almost any sequence of non-commutative random variables that commute or anti-commute pair-wise, the *-moments of the normalized partial sum…
We prove some non-tangential Burns-Krantz type boundary rigidity theorems.
We prove that the non-commutative perspective of an operator convex function is the unique extension of the corresponding commutative perspective that preserves homogeneity and convexity.
We present full classification of Q-conditional symmetries for the two-dimensional nonlinear wave equation.
We reduce the Mathieu conjecture for $SU(2)$ to a conjecture about moments of Laurent polynomials in two variables with single variable polynomial coefficients.
We prove a nonconventional invariance principle (functional central limit theorem) for random fields.
We prove a version of L'hospital's rule for multivariable functions, which holds for non-isolated singular points. We also give an algorithm for resolving many indeterminate limits with isolated singular points.
We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single…
We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations.…
It is a well-known fact that all the statistical predictions of quantum mechanics on the state of any physical system represented by a two-dimensional Hilbert space can always be duplicated by a noncontextual hidden-variables model. In this…
H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.
We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.
An analogue of Gross' logarithmic Sobolev inequality for a class of elements of noncommutative two tori is proved.
We present a simple way to derive the results of Diaconis and Fulman [arXiv:1102.5159] in terms of noncommutative symmetric functions.
We investigate the integrability of the non-commutative leapfrog map in this paper. Firstly, we derive the explicit formula for the non-commutative leapfrog map and corresponding discrete zero-curvature equation by employing the concept of…
In this short note we analyse T-duality properties of non-relativistic String in Torsional Newton-Cartan Background. We also determine condition that ensures that non-relativistic string maps to non-relativistic string under T-duality.
We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Le-Zeilberger. The proofs are combinatorial and new even in the classical cases. We also give…