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Brendan McKay
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This is a classical random walk in the plane, extensively studied wrt Brownian motion etc.. Other people here are more expert in the subject than I am, so I'll leave it for them to provide you with references.

Also, because the summands are bounded, you can apply Hoeffding's inequality or similar to find strong tail bounds.

This is a classical random walk in the plane, extensively studied wrt Brownian motion etc.. Other people here are more expert in the subject than I am, so I'll leave it for them to provide you with references.

This is a classical random walk in the plane, extensively studied wrt Brownian motion etc.. Other people here are more expert in the subject than I am, so I'll leave it for them to provide you with references.

Also, because the summands are bounded, you can apply Hoeffding's inequality or similar to find strong tail bounds.

Source Link
Brendan McKay
  • 37.7k
  • 3
  • 80
  • 147

This is a classical random walk in the plane, extensively studied wrt Brownian motion etc.. Other people here are more expert in the subject than I am, so I'll leave it for them to provide you with references.