Insertion and deletion tolerance of point processes

We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the original process. This condition and the related notion of deletion-tolerance are extensions of the so-called finite energy condition for discrete random processes. We prove several equivalent formulations of each condition, including versions involving Palm processes. Certain other seemingly natural variants of the conditions turn out not to be equivalent. We illustrate the concepts in the context of a number of examples, including Gaussian zero processes and randomly perturbed lattices, and we provide applications to continuum percolation and stable matching

Thermodynamics of Schwarzschild-de Sitter black hole: thermal stability of Nariai black hole

We study thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization, and does not favor the Bousso-Hawking normalization.Comment: 13 pages, 4 figures, version to appear in PR

Poisson splitting by factors

Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that each set of points forms a homogeneous Poisson process, with any given pair of intensities summing to $\lambda$. In particular, this answers a question of Ball [Electron. Commun. Probab. 10 (2005) 60--69], who proved that in $d=1$, the Poisson points may be similarly partitioned (via a translation-equivariant function) so that one set forms a Poisson process of lower intensity, and asked whether the same is possible for all $d$. We do not know whether it is possible similarly to add points (again chosen as a deterministic function of a Poisson process) to obtain a Poisson process of higher intensity, but we prove that this is not possible under an additional finitariness condition.Comment: Published in at http://dx.doi.org/10.1214/11-AOP651 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Deterministic Thinning of Finite Poisson Processes

Let Pi and Gamma be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of Pi and Gamma such that Gamma is a deterministic function of Pi, and all points of Gamma are points of Pi. The condition exhibits a surprising lack of monotonicity. However, in the limit of large intensities, the coupling exists if and only if the expected number of points is at least one greater in Pi than in Gamma.Comment: 16 pages; 1 figur

Surplus Solid Angle as an Imprint of Horava-Lifshitz Gravity

We consider the electrostatic field of a point charge coupled to Horava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly to be obtained in the presence of ordinary matter with positive energy distribution, it seems natural in Horava-Lifshitz gravity. We present the sudden disappearance and reappearance of a star image as an astrophysical effect of a surplus angle. We also consider matter configurations of all possible power law behaviors coupled to Horava-Lifshitz gravity and obtain a series of exact solutions.Comment: 23 pages, 1 figure; minor changes, published versio

Corporate Governance and Management Succession in Family Businesses

Family businesses carry the weight of economic wealth creation in most economies. In the U.S. alone, family businesses account for 80 to 90 percent of the 18-million business enterprises in the United States, and 50 percent of the employment and GNP. In many ways, the family business is synonymous with the entrepreneurial organization as many were started as a means to provide for the financial well being of the founder's family. Founders who went on to build family empires started many of today's large corporations (e.g., Anheuser-Busch, Dupont, and Seagrams). Still, we know relatively little about the issues peculiar to a family business, such as the process and impact of succession planning. Yet, no recurring event in the life of the family firm is more critical to survival than the transfer of power from the incumbent to the successor. Organizations are especially susceptible to loss of vision and purpose during periods of CEO transition, as the leaders who helped shape the vision are replaced by others who may not share the same values and abilities. This study addresses the importance of understanding business succession planning by proposing and empirically verifying a model of succession planning and firm effectiveness in the family business. It links aspects of succession planning and successor preparation to the effectiveness of transition and from performance. The model depicts multiple interactive relationships, with emphasis placed not only on the planning and process-specific but also on successor-specific factors that lead to effectiveness.corporate governance, family businesses, management succession, firm performance, successor characteristics