If I have several accounts in one wallet, can anyone tell they are all connected to the same wallet?

If I have several accounts in one wallet, can anyone tell they are all connected to the same wallet?

Mathematically

Fresh addresses are not connected to each other in any publicly known way. From the outside one can not deduce if an account was created by the same wallet (i.e. Secret Key, also know as “seed phrase”) or not.

Stacks uses points on an elliptic curve for derived addresses. An interesting video about elliptic curves can be found here: https://www.youtube.com/watch?v=NF1pwjL9-DE

From chain analysis

Depending on how you fund the wallet or how your accounts interact with each other someone may be able to tell that they are connected.

For example, if the first account is used to fund another 9 accounts, on-chain analysis will reveal that they are somehow connected via interaction, although they can’t be definitively linked to the same wallet.