Concentrated liquidity pools are a generalisation of the traditional $xy = k$ pool. With the traditional model all users provide liquidity on a $(0, inf)$ price range where as in concentrated liquidity pools each user can pick their own range to provide liquidity on. This allows users to narrow down the liquidity provision range which amplifies their liquidity - meaning traders experience lesser price impact and liquidity providers accrue more fees. This improves capital efficiency by allowing to put more liquidity into a narrow price range, which makes Dfyn more diverse: it can now have pools configured for pairs with different volatility. This is how DfynV2 improves DfynV1.

In a nutshell, a DfynV2 pair is many small DfynV1 pairs. The main difference between V1 and V2 is that, in V2, there are many price ranges in one pair. And each of these shorter price ranges has finite reserves. The entire price range from 0 to infinite is split into shorter price ranges, with each of them having its own amount of liquidity. But, what’s crucial is that within that shorter price ranges, it works exactly as DfynV1 .

Now, let’s try to visualise it. What we’re saying is that we don’t want the curve to be infinite. We cut it at the points aa and bb and say that these are the boundaries of the curve. Moreover, we shift the curve so the boundaries lay on the axes. This is what we get:

Buying or selling tokens moves the price along the curve. A price range limits the movement of the price. When the price moves to either of the points, the pool becomes depleted: one of the token reserves will be 0 and buying this token won’t be possible.

On the chart above, let’s assume that the start price is at the middle of the curve. To get to the point a, we need to buy all available y and maximize x in the range; to get to the point b, we need to buy all available x and maximize y in the range. At these points, there’s only one token in the range.

What happens when the current price range gets depleted during a trade? The price slips into the next price range. If the next price range doesn’t exist, the trade ends up fulfilled partially-we’ll see how this works later in the book.

This is how liquidity is spread in the USDC/ETH pool in production:

You can see that there’s a lot of liquidity around the current price but the further away from it the less liquidity there is–this is because liquidity providers strive to have higher efficiency of their capital. Also, the whole range is not infinite, it’s upper boundary is shown on the image.