相关论文: Explicit Universal Bounds for Cumulants via Moment…

In this work, we study the discrete observables $$E_k = \sum_{i,j=1}^n (i-j)^k A_{i,j}$$ associated with $n\times n$ alternating sign matrices $A = (A_{i,j})$. This work develops exact formulas for expectations using Bernoulli polynomials,…

We prove that if $f(n)$ is a Steinhaus or Rademacher random multiplicative function, there almost surely exist arbitrarily large values of $x$ for which $|\sum_{n \leq x} f(n)| \geq \sqrt{x} (\log\log x)^{1/4+o(1)}$. This is the first such…

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have…

Generally the convergence rate in exponential ergodicity $\lambda$ is an upper bound for the convergence rate $\kappa$ in uniform ergodicity for a Markov process, that is $\lambda\geqslant\kappa$. In this paper, we prove that…

In this paper, we investigate a universal blow-up bound for the focusing mass-critical nonlinear Schr\"odinger equation for general initial data in $L^2(\mathbb R^d)$, extending previous knowledge for mass near the ground-state threshold…

We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $\nu\ne 0$, we also obtain new bounds on exponential sums with $\nu$-th powers of such…

We derive explicit central moment inequalities for random variables that admit a Stein coupling, such as exchangeable pairs, size--bias couplings or local dependence, among others. The bounds are in terms of moments (not necessarily…

It has long been known that random regular graphs are with high probability good expanders. This was first established in the 1980s by Bollob\'as by directly calculating the probability that a set of vertices has small expansion and then…

We are concerned with the general problem of proving the existence of joint distributions of two discrete random variables $M$ and $N$ subject to infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In particular, the…

The introduction of the infinite boundary terms and the pairwise interactions [J. Chem. Theory Comput., 10, 5254, (2014)] enables a physically intuitive approach for deriving electrostatic energy and pressure for both neutral and…

Let $G$ be a group with a non-elementary action on a proper CAT(0) space $X$, and let $\mu$ be a measure on $G$ such that the random walk $(Z_n)_n$ generated by $\mu$ has finite second moment on $X$. Let $o$ be a basepoint in $X$, and…

We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.

Finding the solution to linear ordinary differential equations of the form $\partial_t u(t) = -A(t)u(t)$ has been a promising theoretical avenue for \textit{asymptotic} quantum speedups. However, despite the improvements to existing quantum…

We consider a non-commutative polynomial in several independent $N$-dimensional random unitary matrices, uniformly distributed over the unitary, orthogonal or symmetric groups, and assume that the coefficients are $n$-dimensional matrices.…

In this article, we study the behavior of consecutive values of random completely multiplicative functions $(X_n)_{n \geq 1}$ whose values are i.i.d. at primes. We prove that for $X_2$ uniform on the unit circle, or uniform on the set of…

We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…

We study the statistics of the condition number $\kappa=\lambda_{\mathrm{max}}/\lambda_{\mathrm{min}}$ (the ratio between largest and smallest squared singular values) of $N\times M$ Gaussian random matrices. Using a Coulomb fluid…

We study the lower tail behavior of the least singular value of an $n\times n$ random matrix $M_n := M+N_n$, where $M$ is a fixed complex matrix with operator norm at most $\exp(n^{c})$ and $N_n$ is a random matrix, each of whose entries is…

We study the number of collisions $X_n$ of an exchangeable coalescent with multiple collisions ($\Lambda$-coalescent) which starts with $n$ particles and is driven by rates determined by a finite characteristic measure $\nu({\rm…

Many kinds of independence have been defined in non-commutative probability theory. Natural independence is an important class of independence; this class consists of five independences (tensor, free, Boolean, monotone and anti-monotone…