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Several results point to deep relations between noncommutative geometry and class eld theory ([3], [10], [20], [22]). In [3] a quantum statistical mechanical system (BC) is exhibited, with partition...
An important problem in smooth ergodic theory is to understand an appearance of chaotic behavior in systems governed by deterministic laws. Now it is understood that chaotic behavior is caused by th...
Consider a one parameter family of diffeomorphisms fε such that f0 is an Anosov element in a standard abelian Anosov action having sufficiently strong mixing properties. Let νε be any u-...
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs).
We consider the problem of detecting the true quantum state among r possible ones, based onmeasurements performed on n of copies of a finite dimensional quantum system. It is known that the exponent f...
We consider the decision problem between a finite numberof states of a finite quantum system, when an arbitrarily large number of copies of the system is available for measurements. We provide an uppe...
Gibbs states and the set of solutions of random constraint satisfaction problems.
We consider the Fisher-KPP equation with a nonlocal saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher-KPP equation. Our fir...
We consider the Fisher-KPP equation with a non-local interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions,and prove uniform upper ...
In this paper we develop a general critical point theory to deal with existence and locations of multiple critical points produced by minimax methods in relation to mul-tiple invariant sets of the as...
Dynamics of concentrated polymer solutions are modeled by a Smoluchowski equation. At high concentrations, such solutions form liquid crystalline polymers of nematic structure. We prove that at high i...
In Natural Language Processing (NLP) tasks, data often has the following two properties: First, data can be chopped into multi-views which has been successfully used for dimension reduction purposes. ...
This is the the first of a series of papers considering properties of quantum systems over 2D graphs or manifolds, with continuous spins. In the model considered here the phase space of a single spin ...
We study the nature of the Nonlinear Schr\"odinger equation ground states on the product spaces $\R^n\times M^k$, where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the...
Denote by $J$ the operator of coefficient stripping. We show that for any free convolution semigroup of measures $\nu_t$ with finite variance, applying a single stripping produces semicircular evoluti...

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