Regularity of quasi-stationary measures for simple exclusion in dimension d >= 5

We consider the symmetric simple exclusion process on Z^d, for d>= 5, and study the regularity of the quasi-stationary measures of the dynamics conditionned on not occupying the origin. For each \rho\in ]0,1[, we establish uniqueness of the density of quasi-stationary measures in L^2(d\nur), where \nur is the stationary measure of density \rho. This, in turn, permits us to obtain sharp estimates for P_{\nur}(\tau>t), where \tau is the first time the origin is occupied.Comment: 18 pages. Corrections after referee report. To be published in Ann Proba

Hitting times for independent random walks on Zd\mathbb{Z}^d

We consider a system of asymmetric independent random walks on $\mathbb{Z}^d$, denoted by $\{\eta_t,t\in{\mathbb{R}}\}$, stationary under the product Poisson measure $\nu_{\rho}$ of marginal density $\rho>0$. We fix a pattern $\mathcal{A}$, an increasing local event, and denote by $\tau$ the hitting time of $\mathcal{A}$. By using a loss network representation of our system, at small density, we obtain a coupling between the laws of $\eta_t$ conditioned on $\{\tau>t\}$ for all times $t$. When $d\ge3$, this provides bounds on the rate of convergence of the law of $\eta_t$ conditioned on $\{\tau>t\}$ toward its limiting probability measure as $t$ tends to infinity. We also treat the case where the initial measure is close to $\nu_{\rho}$ without being product.Comment: Published at http://dx.doi.org/10.1214/009117906000000106 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Supersymplectic Homogeneous Superspace Underlying the OSp(1/2) Coherent States

In this work we extend Onofri and Perelomov's coherent states methods to the recently introduced $OSp(1/2)$ coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely the homogeneous superspace $OSp(1/2)/U(1)$, which is clearly identified with a supercoadjoint orbit of $OSp(1/2)$ by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein's supersymplectic supermanifolds. More precisely, we show that its supersymplectic structure is completely determined in terms of $SU(1,1)$-invariant (but unrelated) K\"ahler $2$-form and K\"ahler metric on the unit disc. This result allows us to define the notions of a superK\"ahler supermanifold and a superK\"ahler superpotential, the geometric structure of the former being encoded into the latter.Comment: 19 pgs, PlainTeX, Preprint CRM-185

Minimum BER Precoding in 1-Bit Massive MIMO Systems

1-bit digital-to-analog (DACs) and analog-to-digital converters (ADCs) are gaining more interest in massive MIMO systems for economical and computational efficiency. We present a new precoding technique to mitigate the inter-user-interference (IUI) and the channel distortions in a 1-bit downlink MUMISO system with QPSK symbols. The transmit signal vector is optimized taking into account the 1-bit quantization. We develop a sort of mapping based on a look-up table (LUT) between the input signal and the transmit signal. The LUT is updated for each channel realization. Simulation results show a significant gain in terms of the uncoded bit-error-ratio (BER) compared to the existing linear precoding techniques.Comment: Presented in IEEE SAM 2016, 10th-13th July 2016, Rio De Janeiro, Brazi