اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLevy stable distributions via associated integral transform
128
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{alpha}(x), 0 leq x < infty, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g_{alpha}(x) suffices to obtain exactly g_{alpha^{p}}(x), p=2, 3,... Similarly, from known g_{alpha}(x) and g_{beta}(x), 0 < alpha, beta < 1, we obtain g_{alpha beta}(x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For alpha rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g_{l/k}(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration.
قيم البحث
اقرأ أيضاً
A novel possibility of self-organized behaviour of stochastically driven oscillators is presented. It is shown that synchronization by Levy stable processes is significantly more efficient than that by oscillators with Gaussian statistics. The impact
of outlier events from the tail of the distribution function was examined by artificially introducing a few additional oscillators with very strong coupling strengths and it is found that remarkably even one such rare and extreme event may govern the long term behaviour of the coupled system. In addition to the multiplicative noise component, we have investigated the impact of an external additive Levy distributed noise component on the synchronisation properties of the oscillators.
We study the holomorphic extension associated with power series, i.e., the analytic continuation from the unit disk to the cut-plane $mathbb{C} setminus [1,+infty)$. Analogous results are obtained also in the study of trigonometric series: we establi
sh conditions on the series coefficients which are sufficient to guarantee the series to have a KMS analytic structure. In the case of power series we show the connection between the unique (Carlsonian) interpolation of the coefficients of the series and the Laplace transform of a probability distribution. Finally, we outline a procedure which allows us to obtain a numerical approximation of the jump function across the cut starting from a finite number of power series coefficients. By using the same methodology, the thermal Green functions at real time can be numerically approximated from the knowledge of a finite number of noisy Fourier coefficients in the expansion of the thermal Green functions along the imaginary axis of the complex time plane.
Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions using a cont
inuum time approach by accounting for the statistical distribution through the boundary conditions and using them to evaluate the Greens function.
We study the open version of the su$(m|n)$ supersymmetric Haldane-Shastry spin chain associated to the $BC_N$ extended root system. We first evaluate the models partition function by modding out the dynamical degrees of freedom of the su$(m|n)$ super
symmetric spin Sutherland model of $BC_N$ type, whose spectrum we fully determine. We then construct a generalized partition function depending polynomially on two sets of variables, which yields the standard one when evaluated at a suitable point. We show that this generalized partition function can be written in terms of two variants of the classical skew super Schur polynomials, which admit a combinatorial definition in terms of a new type of skew Young tableaux and border strips (or, equivalently, extended motifs). In this way we derive a remarkable description of the spectrum in terms of this new class of extended motifs, reminiscent of the analogous one for the closed Haldane-Shastry chain. We provide several concretes examples of this description, and in particular study in detail the su$(1|1)$ model finding an analytic expression for its Helmholtz free energy in the thermodynamic limit.
The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability distribution
weighted by an exponential factor whose exponent is uniquely determined by the condition. We apply this theorem to explain the canonical equilibrium ensemble of a system in contact with a heat reservoir. Since the theorem only requires analysis at the level of the function of the subsystem and reservoir, it is applicable even without the knowledge of the composition of the reservoir itself, which extends the applicability of the canonical ensemble. Furthermore, we generalize our theorem to a model with strong interaction that contributes an additional term to the exponent, which is beyond the typical case of approximately additive functions. This result is new in both physics and mathematics, as a theory for the Gibbs conditioning principle for strongly correlated systems. A corollary provides a precise formulation of what a temperature bath is in probabilistic term
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
