Marchenko–Pastur distribution
The Marchenko-Pastur distribution is like a math candy machine that helps us understand things about matrices. Imagine a big bag of candy with lots of different colors, shapes, and sizes. A matrix is like a candy dispenser, where we put the bag of candy in, and it gives us back a set of candies in a specific order and shape.
The Marchenko-Pastur distribution tells us how many candies of each color, shape, and size we can expect to get from the candy dispenser. But it's not just any candy dispenser because the number of candies we get depends on the size and shape of the candy dispenser, and there might be some randomness too!
To make things simple, we can imagine that the candy dispenser is a square shape, and the candy bag has an equal number of candies of each color. The Marchenko-Pastur distribution tells us how many candies we can expect to get of each color, given the size of the square and the number of candies in the bag.
For example, if the candy dispenser is very big, we can expect to get a lot of candies of each color because there's a lot of room for the candy to be dispensed. But if the candy dispenser is very small, we might not get as many candies of each color because there's not enough room for all the candy.
The Marchenko-Pastur distribution is like a formula that helps us calculate how many candies we can expect to get of each color, given the size and shape of the candy dispenser. It's like a magic tool that candy makers can use to make sure they get the right amount of each color candy in their candy dispensed, even if they don't know what colors are in the bag!
Overall, the Marchenko-Pastur distribution helps us understand the candy machine that is the matrix, and predict how many of each color, shape, and size of candy we can expect to get.
The Marchenko-Pastur distribution tells us how many candies of each color, shape, and size we can expect to get from the candy dispenser. But it's not just any candy dispenser because the number of candies we get depends on the size and shape of the candy dispenser, and there might be some randomness too!
To make things simple, we can imagine that the candy dispenser is a square shape, and the candy bag has an equal number of candies of each color. The Marchenko-Pastur distribution tells us how many candies we can expect to get of each color, given the size of the square and the number of candies in the bag.
For example, if the candy dispenser is very big, we can expect to get a lot of candies of each color because there's a lot of room for the candy to be dispensed. But if the candy dispenser is very small, we might not get as many candies of each color because there's not enough room for all the candy.
The Marchenko-Pastur distribution is like a formula that helps us calculate how many candies we can expect to get of each color, given the size and shape of the candy dispenser. It's like a magic tool that candy makers can use to make sure they get the right amount of each color candy in their candy dispensed, even if they don't know what colors are in the bag!
Overall, the Marchenko-Pastur distribution helps us understand the candy machine that is the matrix, and predict how many of each color, shape, and size of candy we can expect to get.