Will my LEGO bricks discolor in indirect sunlight?
I have to disagree somewhat with the other answer in that I do not think it is quite as cut and dried as a simple "no".

There are several factors to consider:


How old is the glass in the windows in the room?
Older glass tends to be less effective at UV diffusion/blocking though really if the glass has been made in the last 50-70 years it's probably fairly safe for UVA, but not necessarily UVB. UVB does not discolor things as quickly but still has an effect. Part of that as well is how many panes are there. Older and/or less expensive windows tend to have fewer panes while newer and/or more expensive windows tend to have more panes and thus more filtering.
What type of glass is in the windows?
If it's just plain clear glass then there is less protection then mirrored, tinted, or specifically UV filtering glass.
(Possibly most importantly) What is the exposure for the windows in the room?
If the windows in the room get a lot of direct exposure (Southern exposure in the Northern hemisphere/Nothern exposure in the Southern hemisphere) then there will just be more UV coming in and thus more discoloration over time. If the room doesn't have a lot of exposure then there will be less. Your pictures seem to indicate that you might not have a lot of direct exposure, but it's hard to tell and even partial exposure (morning or evening light) can make a difference.
Are there some predominant colors being displayed? Some colors, notably White, seem to discolor more noticeably over time. So if you've got a lot of white on display don't plan on it staying pristine for long if you've got a lot of direct exposure in that room.


That all said if you're really worried about it then run some tests to find out. Make a few small stacks of bricks in a few common colors, for example pairs of 2x4 bricks in White, Red, Bley, and Black. Try and make sure you use parts that are very similar in quality, age, and color at the outset. Then place the stacks in various locations. One on the window sill, one on your chosen display location, and one in a closed and opaque box somewhere away from heat sources. Then check on them every couple of weeks and see what results you get. If you haven't seen an appreciable difference between the stored stack and the one in your display area after a month or two you're probably fine. Comparing them against the one in the window sill might even tell you if you'd be safe closer to the window in that particular room. Adding stacks in other locations would just give you more data points to make determinations.

If you do run the test, I would love to see the results. Latitude would also be useful for calibrating your results with what someone else might expect to some extent. :-)