In what way are the main characters of "A & P" and "Araby" initiated into adulthood?This is my thesis so far: In the two stories, both authors...

I think you obviously have a few good ideas to begin with,
but your thesis statement you have supplied doesn't appear to me to be as clear and
concise as it should be. Let me offer a few ideas for you to think about so that you can
perhaps revise it.

One of the central links between these
two brilliant short stories is the way that both protagonists experience an epiphany (a
sudden insight into their actions, motives and characters) at the end of each story that
is linked to their previous actions. Thus it is that the narrator of "A & P," as
he leaves his job, reflects:

readability="13">

Looking back in the big windows, over the bags
of peat moss and aluminum lawn furniture stacked on the pavement, I could see Lengel in
my place in the slot, checking the sheep through. His face was dark grey and his back
stiff, as if he's just had an injection of iron, and my stomach kind of fell as I felt
how hard the world was going to be to me
hereafter.

Having made his
"stand," based on his principles and values, which of course, bring him into conflict
with the rest of the world, Sammy realises the difficult path he has chosen. To continue
being true to himself, he will find that life as a result will not be easy and he will
be placed in other areas where he has to make difficult choices. Going against the flow
is never easy--nor is trying to recoup your
mistakes.

Likewise in "Araby," the unnamed narrator
realises just how naive and romantic he has been when he reaches the bazaar and
experiences the dull reality of something that his dreams and notions had transformed
into an Arabian bazaar full of mystery and magic:

readability="6">

Gazing up into the darkness I saw myself as a
creature driven and derided by vanity; and my eyes burned with anguish and
anger.

Here, the protagonist
realises how stupid he has been and how his illusions and dreams have tainted his
understanding of reality. We recognise that from this point on he will have a more
pragmatic view of life and not be so quick to be overcome by his
dreams.

Thus I would try to revise your thesis statement to
incorporate the way that epiphany functions in both texts to initiate the main
characters into adulthood. Good luck!