# Cramér's Theorem

Cramér's theorem may also refer to another result of the same mathematician concerning the partial sums of a sequence of independent, identically distributed random variables, say X1, X2, X3, …. It is well known, by the law of large numbers, that in this case the sequence

converges in probability to the mean of the probability distribution of Xk. Cramér's theorem in this sense states that the probabilities of "large deviations" away from the mean in this sequence decay exponentially with the rate given by the Cramér function, which is the Legendre transform of the cumulant-generating function of Xk.

### Other articles related to "theorem, theorems":

Robertson–Seymour Theorem
... In graph theory, the Robertson–Seymour theorem (also called the graph minor theorem) states that the undirected graphs, partially ordered by the graph minor ... defined by a finite set of forbidden minors, in the same way that Wagner's theorem characterizes the planar graphs as being the graphs that do not have the complete graph K5 and the complete bipartite graph K3,3 ... The Robertson–Seymour theorem is named after mathematicians Neil Robertson and Paul D ...
Formalized Account of Theorems - Derivation of A Theorem
... The notion of a theorem is very closely connected to its formal proof (also called a "derivation") ... is ABBA The only rule of inference (transformation rule) for is Any occurrence of "A" in a theorem may be replaced by an occurrence of the string "AB ... Theorems in are defined as those formulae which have a derivation ending with that formula ...
Spectral Theorem
... algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices ... In broad terms the spectral theorem provides conditions under which an operator or a matrix can be diagonalized (that is, represented as a diagonal ... In general, the spectral theorem identifies a class of linear operators that can be modelled by multiplication operators, which are as simple as one can hope ...
Spectral Theorem - Bounded Self-adjoint Operators
... also Eigenfunction and Self-adjoint operator#Spectral theorem The next generalization we consider is that of bounded self-adjoint operators on a Hilbert space ... of multiplication by t on L2, that is Theorem ... operator and There is also an analogous spectral theorem for bounded normal operators on Hilbert spaces ...
Robertson–Seymour Theorem - Finite Form of The Graph Minor Theorem
... Friedman, Robertson Seymour (1987) showed that the following theorem exhibits the independence phenomenon by being unprovable in various formal systems that are much stronger than ...

### Famous quotes containing the word theorem:

To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.
Albert Camus (1913–1960)