Hamilton–Jacobi equations for nonsymmetric matrix inference

We study the high-dimensional limit of free energy associated with inference problem a rank-one nonsymmetric matrix. The matrix is expressed as outer product two vectors, not necessarily independent. distributions vectors are only assumed to have scaled bounded supports. bound difference between and solution suitable Hamilton–Jacobi equation in terms much simpler quantities: concentration rate this energy, convergence decoupled system. To demonstrate versatility approach, we apply our result i.i.d. case spherical case. By plugging estimates quantities, identify limits obtain rates.