Breiman said:THEOREM 1. If the random variables W*1, W*2, ... are nonlattice, then for any strategy ...
techmologist said:What does nonlattice mean? Thank you.
SW VandeCarr said:A lattice can be represented by a discrete subspace which spans the vector space [tex]R^n[/tex]. Any point which cannot be generated from the basis vectors by a linear combination with integer coefficients is a non-lattice point (a point with at least one irrational coordinate).
techmologist said:Yeah, that's the only mathematical notion of lattice I am familiar with. Like in crystal structures. But I wasn't sure what it meant in this context: "nonlattice random variables". Is it just a fancy way of saying that the random variables are continuous--or that they attain their limiting values or something like that?
g_edgar said:A "lattice" random variable has all values integer multiples of some one number. This is not the same as "discrete" random variable. For example, if [itex]X[/itex] has only the values 1 and [itex]\sqrt{2}[/itex] is would be discrete but not lattice.
g_edgar said:A "lattice" random variable has all values integer multiples of some one number. This is not the same as "discrete" random variable. For example, if [itex]X[/itex] has only the values 1 and [itex]\sqrt{2}[/itex] is would be discrete but not lattice.
SW Vandecarr said:I don't know. I've seen several papers that use this terminology instead of "continuous". Here's one:
http://econpapers.repec.org/paper/pramprapa/4120.htm
It must have something to do with the modeling of games in terms of "equilibrium sets".
A non-lattice is a type of crystal structure that does not have a well-defined repeating pattern. This means that the atoms or molecules in the structure do not arrange themselves in a predictable and regular manner.
A lattice is a type of crystal structure that has a repeating pattern of atoms or molecules, while a non-lattice does not have this regularity. In a lattice, the building blocks of the crystal are arranged in a specific and predictable way, whereas in a non-lattice, the building blocks may be arranged randomly or in a disordered manner.
Non-lattice structures can be found in a variety of materials, including glasses, polymers, and certain types of alloys. These structures often arise due to the random arrangement of molecules or atoms during the formation of the material.
The structure of a non-lattice is determined through various techniques, such as X-ray diffraction, electron microscopy, and spectroscopy. These methods allow scientists to study the arrangement of atoms or molecules in the material and determine if it has a regular repeating pattern or not.
Non-lattice materials often exhibit unique properties due to their disordered structure. These properties can include high flexibility, low melting points, and high chemical reactivity. Non-lattice materials also have a higher degree of disorder, which can make them more difficult to study and manipulate compared to lattice structures.