Related papers: Dimension and waiting time in rapidly mixing syste…
$D^0-\bar{D}^0$ mixing leads to the mass and width differences in the mass eigenstates of $D^0$ and $\bar{D}^0$ mesons (measured by parameters $x^{~}_D$ and $y^{~}_D$ respectively), but their magnitudes cannot be reliably predicted by the…
Let $x_1,\dots,x_{n}$ be a fixed sequence of real numbers. At each stage, pick $k$ integers $\{I_{i}\}_{1\leq i \leq k}$ uniformly at random without replacement and then for each $i \in \{1,2,\dots,k\}$ replace $x_{I_i}$ by…
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly…
We discuss the theory and phenomenology of $B_{d,s}\to V(\to M_1M_2)\ell\ell$ decays in the presence of neutral-meson mixing. We derive expressions for the time-dependent angular distributions for decays into CP eigenstates, and identify…
Polling systems are a well-established subject in queueing theory. However, their formal treatments generally rely heavily on relatively sophisticated theoretical tools, such as moment generating functions and Laplace transforms, and…
We consider the persistent exclusion process in which a set of persistent random walkers interact via hard-core exclusion on a hypercubic lattice in $d$ dimensions. We work within the ballistic regime whereby particles continue to hop in…
High dimensional central limit theorems (the CLTs) have been extensively studied in recent years under a variety of sufficient moment conditions connecting the dimension growth rate with the tail decay rate. In this article, we investigate…
We identify the integrable stopping time $\tau_*$ with minimal $L^1$-distance to the last-passage time $\gamma_z$ to a given level $z>0$, for an arbitrary non-negative time-homogeneous transient diffusion $X$. We demonstrate that $\tau_*$…
Rare $B$ decays provide an opportunity to probe for new physics beyond the Standard Model. In this paper, we propose to measure the tau polarization in the inclusive decay $B\to X_s\tau^+\tau^-$ and discuss how it can be used, in…
We consider bond percolation on the $d$-dimensional binary hypercube with $p=c/d$ for fixed $c>1$. We prove that the typical diameter of the giant component $L_1$ is of order $\Theta(d)$, and the typical mixing time of the lazy random walk…
In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic…
We prove the Central Limit Theorem and superpolynomial mixing for environment viewed for the particle process in quasi periodic Diophantine random environment. The main ingredients are smoothness estimates for the solution of the Poisson…
The rare decays {$B^- \to \tau \bar\nu$}, \mbox{$B \to \tau^+ \tau^-$}, {$b \to X \nu \bar\nu$} and \mbox{$b \to X \tau^+ \tau^-$} all contain third generation leptons in the final state, and hence are sensitive to new physics that couples…
Assign to each vertex of the one-dimensional torus i.i.d. weights with a heavy-tail of index $\tau-1>0$. Connect then each couple of vertices with probability roughly proportional to the product of their weights and that decays polynomially…
We study the large time behavior of solutions near a constant equilibrium to the compressible Euler-Maxwell system in $\r3$. We first refine a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the…
Analytical considerations and potential flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, $r_n$, decreases as $\tau\propto r_n^2 \, (-\ln{r_n^2})^{1/2}$, where $\tau$ is…
We consider a first-passage percolation model on a Delaunay triangulation of the plane. In this model each edge is independently equipped with a nonnegative random variable, with distribution function F, which is interpreted as the time it…
We study visibility inside the vacant set of three models in $\mathbb R^d$ with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Poisson-Boolean models. Let $Q_x$ be the radius of the largest ball centered…
In this paper, it is shown that for a minimal system $(X,T)$ and $d,k\in \mathbb{N}$, if $(x,x_i)$ is regionally proximal of order $d$ for $1\leq i\leq k$, then $(x,x_1,\ldots,x_k)$ is $(k+1)$-regionally proximal of order $d$. Meanwhile, we…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…