# Martingal

## Definitions

• Webster's Revised Unabridged Dictionary
• Martingal (Naut) A lower stay of rope or chain for the jib boom or flying jib boom, fastened to, or reeved through, the dolphin striker. Also, the dolphin striker itself.
• Martingal A strap fastened to a horse's girth, passing between his fore legs, and fastened to the bit, or now more commonly ending in two rings, through which the reins pass. It is intended to hold down the head of the horse, and prevent him from rearing.
• Martingal (Gambling) The act of doubling, at each stake, that which has been lost on the preceding stake; also, the sum so risked; -- metaphorically derived from the bifurcation of the martingale of a harness. Called also Martingale strategy. Such a betting strategy does not change the overall likelihood of winning, but in a short run it increases the probability of winning a small sum, balancing it against an increased probability of losing a large sum.
• ***

## Etymology

Webster's Revised Unabridged Dictionary
F. martingale,; cf. It. martingala, a sort of hose, martingale, Sp. martingala, a greave, cuish, martingale, Sp. almártaga, a kind of bridle

## Usage

### In science:

The proof of Theorem 1 is based on some combination of the resolvent approach with martingal bounds for the variance of the resolvent traces, used before by many authors, in particularly, by Girko (see and references therein).
Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
Var{Tr G(z )} ≤ C/|ℑz |4 , G(z ) = (M − z )−1 , while in the previous papers the martingal method was used only to obtain the bounds of the type Var{Tr G(z )−1 } ≤ nC (z ).
Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
***