Related papers: The distributivity numbers of of P(om) /fin and it…

We consider natural and general exponential families $(Q_m)_{m\in M}$ on $\mathbb{R}^d$ parametrized by the means. We study the submodels $(Q_{\theta m_1+(1-\theta)m_2})_{\theta\in[0,1]}$ parametrized by a segment in the means domain,…

We consider the following oriented percolation model of $\mathbb {N} \times \mathbb{Z}^d$: we equip $\mathbb {N}\times \mathbb{Z}^d$ with the edge set $\{[(n,x),(n+1,y)] | n\in \mathbb {N}, x,y\in \mathbb{Z}^d\}$, and we say that each edge…

The distributions of the angular transmission coefficient and of the total transmission are calculated for multiple scattered waves. The calculation is based on a mapping to the distribution of eigenvalues of the transmission matrix. The…

The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2. Our…

We investigate the defocusing inhomogeneous nonlinear Schr\"odinger equation $$ i \partial_tu + \Delta u = |x|^{-b} \left({\rm e}^{\alpha|u|^2} - 1- \alpha |u|^2 \right) u, \quad u(0)=u_0, \quad x \in \mathbb{R}^2, $$ with $0<b<1$ and…

We show that in the $\mathbb{P}_{\max}$ extension of a certain Chang-type model of determinacy, if $\kappa\in\{\omega_1, \omega_2, \omega_3\}$, then the restriction of the club filter on $\kappa\cap\mathrm{Cof}(\omega)$ to HOD is an…

We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability…

Given an integer $k\ge2$, let $\omega_k(n)$ denote the number of primes that divide $n$ with multiplicity exactly $k$. We compute the density $e_{k,m}$ of those integers $n$ for which $\omega_k(n)=m$ for every integer $m\ge0$. We also show…

Fundamental solution of a space fractional convection equation of order $\alpha$ is the probability density function of L\'{e}vy flights with long-tailed $\alpha$-stable jump length distribution. By studying an upwind second-order implicit…

Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a…

Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$…

Let the summatory function of the M\"{o}bius function be denoted $M(x)$. We deduce in this article conditional results concerning $M(x)$ assuming the Riemann Hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the…

The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlev\'e II transcendent and its associated isomonodromic system. As a corollary, the density…

We construct a measure on omega-one^2 over the ground model in the forcing extension of a measure algebra, and investigate when measure theoretic properties of some measurable colouring of omega-one^2 imply the existence of an uncountable…

For a pair of distinct non-CM newforms of weights at least 2, having rational integral Fourier coefficients $a_{1}(n)$ and $a_{2}(n)$, under GRH, we obtain an estimate for the set of primes $p$ such that $$ \omega(a_1(p)-a_2(p)) \le […

We focus on the probability distribution function (pdf) $P(\Delta \gamma; \gamma)$ where $\Delta \gamma$ are the {\em measured} strain intervals between plastic events in an athermal strained amorphous solids, and $\gamma$ measures the…

Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\log \mathsf{prt}_{1/8}(f) \cdot…

Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables (not necessarily identically distributed), and $\eta$ be a counting random variable independent of this sequence. We obtain sufficient conditions on…

Let ${\Gamma}_n$ be an $n\times n$ Haar-invariant orthogonal matrix. Let ${ Z}_n$ be the $p\times q$ upper-left submatrix of ${\Gamma}_n$ and ${G}_n$ be a $p\times q$ matrix whose $pq$ entries are independent standard normals, where $p$ and…

If $E$ is an elliptic curve with a point of order two, then work of Klagsbrun and Lemke Oliver shows that the distribution of $\dim_{\mathbb{F}_2}\mathrm{Sel}_\phi(E^d/\mathbb{Q}) - \dim_{\mathbb{F}_2} \mathrm{Sel}_{\hat\phi}(E^{\prime…