scholarly journals A UNIVERSALITY RESULT FOR THE GLOBAL FLUCTUATIONS OF THE EIGENVECTORS OF WIGNER MATRICES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250011 ◽  
Author(s):  
FLORENT BENAYCH-GEORGES
Keyword(s):  
Random Process ◽  
Limit Distribution ◽  
Brownian Bridge ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Wigner Matrix ◽  
The Third ◽  
Necessary And Sufficient ◽  
Global Fluctuations ◽  
Third Moment

We prove that for [Formula: see text] the eigenvectors matrix of a Wigner matrix, under some moments conditions, the bivariate random process [Formula: see text] converges in distribution to a bivariate Brownian bridge. This result has already been proved for GOE and GUE matrices. It is conjectured here that the necessary and sufficient condition, for the result to be true for a general Wigner matrix, is the matching of the moments of orders 1, 2 and 4 of the entries of the Wigner with the ones of a GOE or GUE matrix. Surprisingly, the third moment of the entries of the Wigner matrix has no influence on the limit distribution.

On the convergence of the supercritical branching processes with immigration

1977 ◽  
Vol 14 (2) ◽  
pp. 387-390 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Distribution Function ◽  
Limit Distribution ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Limit Distribution Function ◽  
Branching Process With Immigration ◽  
Necessary And Sufficient ◽  
Supercritical Branching Processes

It is shown for a supercritical branching process with immigration that if the log moment of the immigration distribution is infinite, then no sequence of positive constants {cn} exists such that {Xn/cn} converges in law to a proper limit distribution function F, except for the case F(0 +) = 1. Seneta's result [1] combined with the above-mentioned one imply that if 1 < m < ∞ then the finiteness of the log moment of the immigration distribution is a necessary and sufficient condition for the existence of some constants {cn} such that {Xn/cn} converges in law to a proper limit distribution function F, with F(0 +) < 1.

scholarly journals Six-dimensional considerations of Einstein's connection for the first two classes. II. The Einstein's connection in6-g-UFT

1999 ◽  
Vol 22 (3) ◽  
pp. 483-488
Author(s):  
Kyung Tae Chung ◽  
Gye Tak Yang ◽  
In Ho Hwang
Keyword(s):  
Field Theory ◽  
Recurrence Relations ◽  
Sufficient Condition ◽  
Field Tensor ◽  
Necessary And Sufficient Condition ◽  
Unified Field Theory ◽  
The Third ◽  
Unified Field ◽  
Necessary And Sufficient ◽  
Lower Dimensional

Lower dimensional cases of Einstein's connection were already investigated by many authors forn=2,3,4,5. In the following series of two papers, we present a surveyable tensorial representation of6-dimensional Einstein's connection in terms of the unified field tensor:I. The recurrence relations in6-g-UFT.II. The Einstein's connection in6-g-UFT.In our previous paper [2], we investigated some algebraic structure in Einstein's6-dimensional unified field theory (i.e.,6-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in6-g-UFT. This paper is a direct continuation of [2]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in6-g-UFT and to display a surveyable tensorial representation of6-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [2].All considerations in this paper are restricted to the first and second classes of the6-dimensional generalized Riemannian manifoldX6, since the case of the third class, the simplest case, was already studied by many authors.

scholarly journals (1, 2) AND WEAK (1, 3) HOMOTOPIES ON KNOT PROJECTIONS

2013 ◽  
Vol 22 (14) ◽  
pp. 1350085 ◽  
Author(s):  
NOBORU ITO ◽  
YUSUKE TAKIMURA
Keyword(s):  
Equivalence Relation ◽  
Finite Sequence ◽  
Reidemeister Move ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Homotopy Classes ◽  
The Third ◽  
Reidemeister Moves ◽  
Necessary And Sufficient

In this paper, we obtain the necessary and sufficient condition that two knot projections are related by a finite sequence of the first and second flat Reidemeister moves (Theorem 2.2). We also consider an equivalence relation that is called weak (1, 3) homotopy. This equivalence relation occurs by the first flat Reidemeister move and one of the third flat Reidemeister moves. We introduce a map sending weak (1, 3) homotopy classes to knot isotopy classes (Sec. 3). Using the map, we determine which knot projections are trivialized under weak (1, 3) homotopy (Corollary 4.1).

scholarly journals Seven-dimensional considerations of Einstein's connection. III. The seven-dimensional Einstein's connection

2003 ◽  
Vol 2003 (15) ◽  
pp. 947-958
Author(s):  
Mi Ae Kim ◽  
Keum Sook So ◽  
Chung Hyun Cho ◽  
Kyung Tae Chung
Keyword(s):  
Recurrence Relations ◽  
Sufficient Condition ◽  
Field Tensor ◽  
Necessary And Sufficient Condition ◽  
The Third ◽  
Unified Field ◽  
Necessary And Sufficient

The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in7-g-UFT and to display a surveyable tensorial representation of seven-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in earlier papers. All considerations in this paper are restricted to the first and second classes ofX7, since the case of the third class, the simplest case, was already studied by many authors.

On the convergence of the supercritical branching processes with immigration

1977 ◽  
Vol 14 (02) ◽  
pp. 387-390 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Distribution Function ◽  
Limit Distribution ◽  
Branching Process ◽  
Branching Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Limit Distribution Function ◽  
Branching Process With Immigration ◽  
Necessary And Sufficient ◽  
Supercritical Branching Processes

It is shown for a supercritical branching process with immigration that if the log moment of the immigration distribution is infinite, then no sequence of positive constants {cn } exists such that {Xn/cn } converges in law to a proper limit distribution function F, except for the case F(0 +) = 1. Seneta's result [1] combined with the above-mentioned one imply that if 1 &lt; m &lt; ∞ then the finiteness of the log moment of the immigration distribution is a necessary and sufficient condition for the existence of some constants {cn } such that {Xn /c n} converges in law to a proper limit distribution function F, with F(0 +) &lt; 1.

scholarly journals Note on limit distribution of normalized return times and escape rate

2016 ◽  
Vol 16 (03) ◽  
pp. 1660014 ◽  
Author(s):  
Xuan Zhang
Keyword(s):  
Decay Rate ◽  
Exponential Decay ◽  
Limit Distribution ◽  
Escape Rate ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Return Times ◽  
Exponential Decay Rate ◽  
Necessary And Sufficient

In this note we discuss limit distribution of normalized return times for shrinking targets and draw a necessary and sufficient condition using sweep-out sequence in order for the limit distribution to be exponential with parameter 1. The normalizing coefficients are the same as the sizes of the targets. Moreover we study escape rate, namely the exponential decay rate of sweep-out sequence and prove that in [Formula: see text]-mixing systems for a certain class of sets the escape rate is in limit proportional to the size of the set.

scholarly journals Unions of Cockcroft two-complexes

1994 ◽  
Vol 37 (2) ◽  
pp. 317-324
Author(s):  
W. A. Bogley
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Third ◽  
Necessary And Sufficient

A combinatorial hypothesis is presented that serves as a necessary and sufficient condition for a union of connected Cockcroft two-complexes to be Cockcroft. This combinatorial hypothesis has a component that can be expressed in terms of the second homology of groups. The hypothesis is applied to the study of the third homology of groups.

Sign in / Sign up

Export Citation Format

Share Document