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Definition of non-lattice

  1. Aug 4, 2010 #1
    definition of "non-lattice"

    In section 3 of this paper (bottom of 4th page):


    What does nonlattice mean? Thank you.
  2. jcsd
  3. Aug 5, 2010 #2
    Re: definition of "non-lattice"

    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).
  4. Aug 5, 2010 #3
    Re: definition of "non-lattice"

    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?
  5. Aug 5, 2010 #4
    Re: definition of "non-lattice"

    I don't know. I've seen several papers that use this terminology instead of "continuous". Here's one:


    It must have something to do with the modeling of games in terms of "equilibrium sets".
  6. Aug 5, 2010 #5
    Re: definition of "non-lattice"

    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.
  7. Aug 5, 2010 #6
    Re: definition of "non-lattice"

    OK. So a discrete RV can be non-lattice provided it ranges over a countable set? (It's a rhetorical question. No need to respond unless you disagree.) Thanks.
    Last edited: Aug 5, 2010
  8. Aug 5, 2010 #7
    Re: definition of "non-lattice"

    Thank you for that definition :).

    Thanks for the link.
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