Large deviation principle

Okay, so imagine you have some favorite toys that you like to play with. Let's say you have 10 blocks and you like to build towers with them. Sometimes you build really tall towers with all 10 blocks, and sometimes you only use a few blocks to build small towers.

Now, let's say you build towers with your blocks every day for a month. You might notice that some days you build really tall towers, and other days you only build small ones. But overall, you might notice that you tend to build towers that are a certain size most of the time.

That's kind of like what happens with large deviation principle. It's a way of looking at how something behaves over a long period of time, and figuring out what the most likely outcome is.

For example, let's say you wanted to take a walk every day for a month, and you wanted to know how far you were most likely to walk each day. The large deviation principle would tell you that you're most likely to walk a certain distance (maybe a mile or two), but some days you might walk farther and some days you might walk less. The principle helps you figure out how likely those more extreme outcomes are.

So basically, the large deviation principle is a way of studying the probability of rare events happening over a long period of time. It helps us understand what the most likely outcome is, but also how likely it is that more unusual outcomes might occur.