USC Geography grad Samuel Krueger's thesis, "Delimiting the Postmodern Urban Center: An Analysis of Urban Amenity Clusters in Los Angeles," shows that LA does have a strong core center which runs from Santa Monica to DTLA. He dubbed it The Wilshire/Santa Monica Corridor –it's named for the "two main arteries along which the city's center is concentrated."
Does it even matter? What's the point? Samuel wanted to show that LA is just like any other major city – it has a cultural center.