noise added to the matrix and delta p is the noise added to the tensor so the bigger the noise the harder this inference problem will be and for instance if the delta p was infinity that would be effectively as if the tensor was not there it's not giving you any information so in that case you are in the case of spiked matrix factorization that is problem widely studied in statistics and you know it has the bbp phase transition and that's precisely what the value lambda 2 equal to 1 corresponds to so that's what