Does changing state cause re-render in ReactJS

In my ReactJS application, I have an array of dictionaries stored as a state called items that looks like this:

this.state = {
   items: []
}

I then add items to the list after certain events, ex: click a button, which causes this.state.items to continue to grow to look like something like this:

items: [{"item": "milk", "price": 3.00}, {"item": "eggs", "price": 5.00}]

The items state directly influences my UI because

this.state.items.map((item, i) => <><h1>{item.item}</h1><p>{item.price}</p></>)

My question is: Is this causing my UI to have to re-render items in the items list that have already been renders every time the items state changes. If so, how do I fix that?

Thank you!