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In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…

In [Bailo, Carrillo, Hu. SIAM J. Appl. Math. 2023] the authors introduce a finite-volume method for aggregation-diffusion equations with non-linear mobility. In this paper we prove convergence of this method using an Aubin--Simons…

We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the…

This work concerns about forward-backward multivalued stochastic systems. First of all, we prove one average principle for general stochastic differential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ a convergence rate…

We establish convergence in norm and pointwise almost everywhere for the non-conventional (in the sense of Furstenberg) bilinear polynomial ergodic averages \[ A_N(f,g)(x) := \frac{1}{N} \sum_{n =1}^N f(T^nx) g(T^{P(n)}x)\] as $N \to…

In this paper we are discussing the question how a continuous quantum system can be simulated by mean field fluctuations of a finite number of qubits. On the kinematical side this leads to a convergence result which states that…

We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order…

Let $\Sigma_{A}$ be a topologically mixing shift of finite type, let $\sigma:\Sigma_{A}\to\Sigma_{A}$ be the usual left-shift, and let $\mu$ be the Gibbs measure for a H\"{o}lder continuous potential that is not cohomologous to a constant.…

Macroscopic observables in a quantum spin system are given by sequences of spatial means of local elements $\frac{1}{2n+1}\sum_{j=-n}^n\gamma_j(A_{i}), \; n\in{\mathbb N},\; i=1,...,m$ in a UHF algebra. One of their properties is that they…

``Fuzzy CP^2'', which is a four-dimensional fuzzy manifold extension of the well-known fuzzy analogous to the fuzzy 2-sphere (S^2), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving…

It is shown that the cubic nonconventional ergodic average of order 2 with M\"obius and Liouville weight converge almost surely to zero. As a consequence, we obtain that the Ces\`aro mean of the self-correlations and some moving average of…

We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting…

The purpose of this paper is to study ergodic averages with deterministic weights. More precisely we study the convergence of the ergodic averages of the type $\frac{1}{N} \sum_{k=0}^{N-1} \theta (k) f \circ T^{u_k}$ where $\theta = (\theta…

In this article we prove that given a self-similar interval exchange transformation T, whose associated matrix verifies a quite general algebraic condition, there exists an affine interval exchange transformation with wandering intervals…

We prove that if a sequence of pairs of smooth commuting Hamiltonians converge in the $C^0$ topology to a pair of smooth Hamiltonians, these commute. This allows us define the notion of commuting continuous Hamiltonians. As an application…

Rigorous assessment of the uncertainty is crucial to the utility of numerical simulation of Turbulent flow. The Turbulent flows are often stationary and ergodic, after some initial transient time. Therefore, the time averaged of a quantity…

Let X be a metric space with metric d and T,S be two commutative measure-preserving maps of X. In this paper we obtain numerical results about multiple recurrence of almost every point of this dynamical system. On other words we study the…

Let $F$ be a Hecke-Maass cusp form for $\mathrm{SL}_3(\mathbb{Z})$ and $A(m,n)$ be its normalized Fourier coefficients. Let $V$ be a smooth function, compactly supported on $[1,2]$ and satisfying $V(y)^{j} \ll_j y^{-j}$ for any $j \in…

The commuting probability of a finite group is defined to be the probability that two randomly chosen group elements commute. Let P \subset (0,1] be the set of commuting probabilities of all finite groups. We prove that every point of P is…

We explicitly construct noncommutative * products on circularly symmetric two dimensional space by using the technique of Fedosov's deformation quantization. Especially, on constant curvature spaces i.e., S^2 and H^2, we get su(2) and…