An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation

Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

The SU(3) bosons and the spin nematic state on the spin-1 bilinear-biquadratic triangular lattice

A bond-operator mean-field theory in the SU(3) bosons representation is developed to describe the antiferro-nematic phase of the spin-1 bilinear-biquadratic model. The calculated static structure factors reveal delicately that the antiferro-nematic state may exhibit both the ferro- and antiferro-quadruple long-range orders, which is reminiscent of the ferrimagnets or the canted antiferromagnets. This result may influence the spin wave theory concerned with this phase. Possible relevance of this unconventional state to the quasi-two-dimensional triangular material NiGa2S4 is addressed.Comment: 8pages, 6figure

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

Should I Stay or Should I go? Founder Power and Exit via Initial Public Offering

Founders can voluntarily exit their ventures via initial public offerings (IPOs). In this study, we build on power theory to develop and test a model of founder exit using a dataset of 313 founders from 177 entrepreneurial IPOs between 2002 and 2010. We largely find support for the model—a negative relationship between founder power and full exit. To capture the underlying mechanism of the power-exit relationship, we conducted two experiments in which we randomly assigned decision makers to either a high- or low-power condition. We find that decision makers in the low-power condition are more likely to use a full exit via IPO than those in the high-power condition and that frustration mediates this relationship. However, founders can also engage in partial exits, including a managerial partial exit in which the founder leaves management but keeps ownership and a financial partial exit in which the founder divests ownership but remains in management. We find that the negative relationship between founder power and exit is more negative for full exits than partial exits. With this paper, we contribute to the literature on exit by identifying a novel mechanism—frustration—underlying power’s influence on the likelihood and type of founder exit

Translation-symmetry protected topological orders on lattice

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 sub-classes corresponding to 16 new translation-symmetry protected topological orders. We introduced four $Z_2$ topological indices $\zeta_{\v{k}}=0,1$ at $\v {k}=(0,0)$, $(0,\pi)$, $(\pi, 0)$, $(\pi ,\pi)$ to characterize those 16 new topological orders. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on 3D lattice

Controlled MOCVD growth of Bi2Se3 topological insulator nanoribbons

Topological insulators are a new class of materials that support topologically protected electronic surface states. Potential applications of the surface states in low dissipation electronic devices have motivated efforts to create nanoscale samples with large surface-to-volume ratios and highly controlled stoichiometry. Se vacancies in Bi2Se3 give rise to bulk conduction, which masks the transport properties of the surface states. We have therefore developed a new route for the synthesis of topological insulator nanostructures using metalorganic chemical vapour deposition (MOCVD). MOCVD allows for control of the Se/Bi flux ratio during growth. With the aim of rational growth, we vary the Se/Bi flux ratio, growth time, and substrate temperature, and observe morphological changes which indicate a growth regime in which nanoribbon formation is limited by the Bi precursor mass-flow. MOCVD growth of Bi2Se3 nanostructures occurs via a distinct growth mechanism that is nucleated by gold nanoparticles at the base of the nanowire. By tuning the reaction conditions, we obtain either single-crystalline ribbons up to 10 microns long or thin micron-sized platelets.Comment: Related papers at http://pettagroup.princeton.ed

Composite absorbing potentials

The multiple scattering interferences due to the addition of several contiguous potential units are used to construct composite absorbing potentials that absorb at an arbitrary set of incident momenta or for a broad momentum interval.Comment: 9 pages, Revtex, 2 postscript figures. Accepted in Phys. Rev. Let

Power-law behavior in the power spectrum induced by Brownian motion of a domain wall

We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $\omega^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.Comment: 4 pages, 4 figure