Decomposition of Levy trees along their diameter

We study the diameter of L{\'e}vy trees that are random compact metric spaces obtained as the scaling limits of Galton-Watson trees. L{\'e}vy trees have been introduced by Le Gall and Le Jan (1998) and they generalise Aldous' Continuum Random Tree (1991) that corresponds to the Brownian case. We first characterize the law of the diameter of L{\'e}vy trees and we prove that it is realized by a unique pair of points. We prove that the law of L{\'e}vy trees conditioned to have a fixed diameter r $\in$ (0, $\infty$) is obtained by glueing at their respective roots two independent size-biased L{\'e}vy trees conditioned to have height r/2 and then by uniformly re-rooting the resulting tree; we also describe by a Poisson point measure the law of the subtrees that are grafted on the diameter. As an application of this decomposition of L{\'e}vy trees according to their diameter, we characterize the joint law of the height and the diameter of stable L{\'e}vy trees conditioned by their total mass; we also provide asymptotic expansions of the law of the height and of the diameter of such normalised stable trees, which generalises the identity due to Szekeres (1983) in the Brownian case

Accurate detection of moving targets via random sensor arrays and Kerdock codes

The detection and parameter estimation of moving targets is one of the most important tasks in radar. Arrays of randomly distributed antennas have been popular for this purpose for about half a century. Yet, surprisingly little rigorous mathematical theory exists for random arrays that addresses fundamental question such as how many targets can be recovered, at what resolution, at which noise level, and with which algorithm. In a different line of research in radar, mathematicians and engineers have invested significant effort into the design of radar transmission waveforms which satisfy various desirable properties. In this paper we bring these two seemingly unrelated areas together. Using tools from compressive sensing we derive a theoretical framework for the recovery of targets in the azimuth-range-Doppler domain via random antennas arrays. In one manifestation of our theory we use Kerdock codes as transmission waveforms and exploit some of their peculiar properties in our analysis. Our paper provides two main contributions: (i) We derive the first rigorous mathematical theory for the detection of moving targets using random sensor arrays. (ii) The transmitted waveforms satisfy a variety of properties that are very desirable and important from a practical viewpoint. Thus our approach does not just lead to useful theoretical insights, but is also of practical importance. Various extensions of our results are derived and numerical simulations confirming our theory are presented

Probing beyond ETH at large cc

We study probe corrections to the Eigenstate Thermalization Hypothesis (ETH) in the context of 2D CFTs with large central charge and a sparse spectrum of low dimension operators. In particular, we focus on observables in the form of non-local composite operators $\mathcal{O}_{obs}(x)=\mathcal{O}_L(x)\mathcal{O}_L(0)$ with $h_L\ll c$. As a light probe, $\mathcal{O}_{obs}(x)$ is constrained by ETH and satisfies $\langle \mathcal{O}_{obs}(x)\rangle_{h_H}\approx \langle \mathcal{O}_{obs}(x)\rangle_{\text{micro}}$ for a high energy energy eigenstate $| h_H\rangle$. In the CFTs of interests, $\langle \mathcal{O}_{obs}(x)\rangle_{h_H}$ is related to a Heavy-Heavy-Light-Light (HL) correlator, and can be approximated by the vacuum Virasoro block, which we focus on computing. A sharp consequence of ETH for $\mathcal{O}_{obs}(x)$ is the so called "forbidden singularities", arising from the emergent thermal periodicity in imaginary time. Using the monodromy method, we show that finite probe corrections of the form $\mathcal{O}(h_L/c)$ drastically alter both sides of the ETH equality, replacing each thermal singularity with a pair of branch-cuts. Via the branch-cuts, the vacuum blocks are connected to infinitely many additional "saddles". We discuss and verify how such violent modification in analytic structure leads to a natural guess for the blocks at finite $c$: a series of zeros that condense into branch cuts as $c\to\infty$. We also discuss some interesting evidences connecting these to the Stoke's phenomena, which are non-perturbative $e^{-c}$ effects. As a related aspect of these probe modifications, we also compute the Renyi-entropy $S_n$ in high energy eigenstates on a circle. For subsystems much larger than the thermal length, we obtain a WKB solution to the monodromy problem, and deduce from this the entanglement spectrum.Comment: 35 pages, 40 figures, additional results and comments adde

Phase transition from hadronic matter to quark matter

We study the phase transition from nuclear matter to quark matter within the SU(3) quark mean field model and NJL model. The SU(3) quark mean field model is used to give the equation of state for nuclear matter, while the equation of state for color superconducting quark matter is calculated within the NJL model. It is found that at low temperature, the phase transition from nuclear to color superconducting quark matter will take place when the density is of order 2.5$\rho_0$ - 5$\rho_0$. At zero density, the quark phase will appear when the temperature is larger than about 148 MeV. The phase transition from nuclear matter to quark matter is always first order, whereas the transition between color superconducting quark matter and normal quark matter is second order.Comment: 18 pages, 11 figure

The Dynamics of Chinese Rural Households' Participation in Labor Markets

The work focuses on the frequency of each possible transition between labor market participation regimes of rural Chinese households. A continuous hazard approach is applied to empirically evaluate factors, as household, farm, and regional characteristics affecting the frequency of transition between labor market participation states. Results suggest that there are frequent changes of labor market participations regimes among the househo lds. Given the change in external conditions and other factor end owments this might indicate that households quickly response in allocating labor in order to equilibrate the resources. Further, we find that there are good chances climbing out of autarky; however the probability to fall in autarky was also remarkable over time.Labor market participation, dynamic analysis, China, hazard model, rural households, Labor and Human Capital, C41, J60, Q12,

The Persistence of Poverty in Rural China: Applying an Ordered Probit and a Hazard Approach

The present study investigates the analysis of poverty persistence of Chinese farm households in the well-off Zhejiang province in the southeast. We firstly apply an ordered probit model examining household, farm, and regional characteristics affecting the probability that households are chronically poor. In addition, we apply a hazard approach to identify the risk of falling into and climbing out of poverty. Results indicate that there are increasing chances to climb out of poverty over time, and that the risk of falling into poverty seems to decrease after the household spent some time outside poverty.Poverty persistence, China, rural population, hazard analysis, dynamics, Food Security and Poverty, C23, D1, I32, R29,

Labor Market Participation of Chinese Agricultural Households

This work is devoted to the analysis of the different labor market participation regimes of Chinese farm households. Using household data over the period 1986-2000 from the province Zhejiang, we apply a multinomial logit model to empirically examine household, farm, and regional characteristics affecting the probability that farmers employ one of four alternative labor market regimes. Results suggest that labor market decisions are significantly related to several personal, farm, and village attitudes. In addition, we find the more market oriented policy reforms at the end of the 1980s stipulated that households participate in labor markets while the more anti-market reforms during the 1990s led to the opposite and encouraged autarky.China, labor markets, agricultural household, participation, multinomial logit, Consumer/Household Economics, Labor and Human Capital, D13, J24, J43, Q12,

Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques

We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent equations are solved on a heirarchy of grids of increasing resolution with a nonlinear Full Approximation Scheme, Full Multigrid algorithm. The self consistency is effected by updates of the Poisson equation and the exchange correlation potential at the end of each eigenfunction correction cycle. The algorithm leads to highly efficient solution of the equations, whereby the ground state electron distribution is obtained in only two or three self consistency iterations on the finest scale.Comment: 13 pages, 2 figure