User:Sylvain Ribault/Bootstat2021/Su

Navigator function could replace other numerical bootstrap methods.

Numerical bootstap leads to islands in parameter space, allowed by crossing symmetry constraints.

Traditional method

Look for functional that is positive when acting on a number of (combinations of) blocks. For a given cutoff we want to find an allowed point, and map the island to which it belongs. Then we increase the cutoff. If we increase the cutoff too much, the corresponding island is too small and we may not find a point in it. In practice it is painful, need tricks to find an allowed point. If dimension of parameter space is large, it is hard to explore. And bootstrap is about exploring unknowns: traditional method requires us to know something from start, and we might miss some small island.

Navigator approach

Test a point in parameter space, then a navigator tells us which direction to go in order to get closer to the island. The navigator is a function that is negative in allowed region, positive in infeasible region.

Navigator function is value of the functional on the identity block, for a functional that maximizes that value under some constraints?