The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents.
- excerpt from The Call of Cthulhu

    This quote, above all others, perfectly exemplifies H.P. Lovecraft's works' mood: one of powerlessness, of powers above human comprehension.

   One of his creations, the character Randpolph Carter, gives us an evem more specific insight into many of Lovecraft's other works, as he himself has been featured in seven of them.
Carter is an antiquarian, as well as an author of strange fiction and discoverer of many discoveries alike.

    Carter was born around the year 1874 in the Boston area. a descendant of Sir Randolph Carter, who studied magic during Queen Elizabeth Is reign, and immigrated to America, only to flee during the Salem Witch Trials. Carter also served in French Foreign Legion in World War 1. He was later wounded and discharged. Carter then returned to the New England area, where Lovecraft's writings of him begin.

Carter himself, is speculated to be a semi-autobiographical character, representing Lovecraft himself in many ways.
Carter's journey to regain his dreams may be connected to Lovecraft's overwhelming anxiety at an early age.
The Statement of Randolph Carter, as well as other stories such as The Shadow over Innsmouth, may be yet another philosophical tie to his life, related to the early death of his mother due to depression and hysteria, or possibly his feelings against society as a whole.

The physical being of Randolph Carter is never described in detail, and this is reflected in the various visual depictions taken by fans, especially in films.

Carter in The Testimony of Randolph Carter
      Carter's appearance in "The Testimony of Randolph Carter"
Carter in The Unnamable
Carter in "The Unnamable"
Carter in The Dream-Quest Of Unknown Kadath
A depiction of Carter by Alan Brown
Carter in The Statement of Randolph Carter
Carter in the film "The Statement of Randolph Carter" By Jason Hunt

   As you can see, these depictions of Carter share some traits: dark, short hair, a more formal style of dress, and a young age. However, the differences are more striking.
In Jason Hunt's depiction of Carter, he is shown to have a sort of distraught look to him, while in the image from "The Unnamable", Carter has a sort of aloof expression on his face (as well as eyewear), as if he was confident about what was to happen.
In the shot of "The Testimony of Randolph Carter", he is shown to have a sort of dirty-blonde hair, along with being dressed in very formal clothes, which is surprising considering the events that had just taken place.
Furthermore, in Alan Brown's illustration of Carter during "The Dream-Quest of Unknown Kadath", Carter is very much older, and features a full-grown beard along with a somewhat-dressy, yet formal style, accompanied with thigh-high boots - suitable for the journey he had embarked upon.

   As far as Carter's personality, Lovecraft left us much more to work with, as is the nature of Lovecraft's work; that of the written work. Through his actions, we can accurately predict that Carter is confident, as his actions during "The Statement of Randolph Carter", as well as the willpower he demonstrated in "The Silver Key".